First, to directly answer your question. No, the scriptures do not overtly say that every cell in your body has its own individual atman. Conversely they do not say that they carry only ‘your’ one atman. This is because the object of scriptures, the purpose of Vedanta, is to establish the reality of Brahman as the ultimate Reality; it is not the purpose of the scriptures to define or explain every aspect of Maya in minutiae. Sankaracharya says in his commentary on Brahma Sutras (II. iii. 21), Swami Vireswarananda translator (available here - http://www.wisdomlib.org/hinduism/book/brahma-sutras/d/doc62753.html):
If it be said (that the soul is) not atomic, as the scriptures state it to otherwise (i.e. all pervading), (we say) not so, for (the one) other than the individual soul (i.e. Supreme Brahman) is the subject –matter (in those texts).
Sruti texts like, “He is the one God…all pervading” (Svetasvatara U. 6.11), refer not to the individual soul, but to the Supreme Lord, who is other than the individual soul and forms the chief subject matter of all the Vedanta texts; for that is the one thing that is to be known, and is therefore propounded by all the Vedanta texts.
The rishis and sages of the past were not concerned in knowing every form of clay, of Maya, there exists within the universe of Maya endless names and forms, they were concerned in knowing about the source of the clay, the source of these names and forms. Material knowledge gained through the material sciences over the last 200-300 hundred years, notably microbiology, has made us aware of the existence of life at a microscopic level. Scripture, however, has given us the means to understand. Scripture breaks the universe, Maya, into two components – sentient and insentient. To understand this difference, see my answer to this question - What is the difference between living beings and dead matter according to scriptures?
We also read in the Taittiriya Upanishad II. vi. 1 (Swami Gambhirananda translator):
…That (Brahman) having created (that), entered into that very thing. And having entered there, It became the formed and the formless, the defined and the undefined, the sustaining and non-sustaining, the sentient and the insentient, the true and the untrue…
And Sankara’s commentary on this verse says in part:
…Vijnanam is sentient, and avijnanam is devoid of sentience, insentient stone etc…
And Sri Vidyaranya Swami says in his Pancadasi IV.10 (Swami Swahananda translator):
According to these Srutis Brahman or Atman Himself, assuming manifold forms as the Jivas, entered into these bodies. A Jiva is so called because it upholds vitality (the Pranas) (in a body).
And Swahananda commentary on this verse:
‘Jiva’ literally means a living being, or the principle of life.
And in the Brhadaranyaka Upanishad I. iv. (Swami Madhavananda translator) we read:
…this Self has entered into these bodies up to the tip of the nails—as a razor may be put into a case,…People do not see It, for (viewed in Its aspects) It is incomplete. When It does the function of the living, It is called the vital force…
The question then becomes are individual cells sentient or insentient? Do they contain their own vital force, their own prana? We can separate individual cells from the body, and we (as a body) continue to live without those individual cells, and they can continue to sustain their own separate lives. They require their own food and oxygen to continue, and we can make them respond to outside stimuli – they ‘perceive’ – their own rudimentary consciousness - i.e. they have their own vitality, own vital force, the Pranas spoken of above; we can then conclude that they have their own individual sentence, that these individual cells are not devoid of sentence. They are not rocks, stones, etc., and therefore have their own individual atmans.
Swami Vivekananda says (Complete Works, V2, pp 208-209, available here under the heading Jnana Yoga, sub-heading The Cosmos: The Macrocosm - http://cwsv.belurmath.org/volume_2/vol_2_frame.htm):
We see then, that nothing can be created out of nothing. Everything exists through eternity, and will exist through eternity. Only the movement is in succeeding waves and hollows, going back to fine forms, and coming out into gross manifestations. This involution and evolution is going on throughout the whole of nature. The whole series of evolution beginning with the lowest manifestation of life and reaching up to the highest, the most perfect man, must have been the involution of something else. The question is: The involution of what? What was involved? God. The evolutionist will tell you that your idea that it was God is wrong. Why? Because you see God is intelligent, but we find that intelligence develops much later on in the course of evolution. It is in man and the higher animals that we find intelligence, but millions of years have passed in this world before this intelligence came. This objection of the evolutionists does not hold water, as we shall see by applying our theory. The tree comes out of the seed, goes back to the seed; the beginning and the end are the same. The earth comes out of its cause and returns to it. We know that if we can find the beginning we can find the end. E converso, if we find the end we can find the beginning. If that is so, take this whole evolutionary series, from the protoplasm at one end to the perfect man at the other, and this whole series is one life. In the end we find the perfect man, so in the beginning it must have been the same. Therefore, the protoplasm was the involution of the highest intelligence. You may not see it but that involved intelligence is what is uncoiling itself until it becomes manifested in the most perfect man. That can be mathematically demonstrated. If the law of conservation of energy is true, you cannot get anything out of a machine unless you put it in there first. The amount of work that you get out of an engine is exactly the same as you have put into it in the form of water and coal, neither more nor less. The work I am doing now is just what I put into me, in the shape of air, food, and other things. It is only a question of change and manifestation. There cannot be added in the economy of this universe one particle of matter or one foot-pound of force, nor can one particle of matter or one foot-pound of force be taken out. If that be the case, what is this intelligence? If it was not present in the protoplasm, it must have come all of a sudden, something coming out of nothing, which is absurd. It, therefore, follows absolutely that the perfect man, the free man, the God-man, who has gone beyond the laws of nature, and transcended everything, who has no more to go through this process of evolution, through birth and death, that man called the "Christ-man" by the Christians, and the "Buddha-man" by the Buddhists, and the "Free" by the Yogis — that perfect man who is at one end of the chain of evolution was involved in the cell of the protoplasm, which is at the other end of the same chain.
Applying the same reason to the whole of the universe, we see that intelligence must be the Lord of creation, the cause. What is the most evolved notion that man has of this universe? It is intelligence, the adjustment of part to part, the display of intelligence, of which the ancient design theory was an attempt at expression. The beginning was, therefore, intelligence. At the beginning that intelligence becomes involved, and in the end that intelligence gets evolved. The sum total of the intelligence displayed in the universe must, therefore, be the involved universal intelligence unfolding itself. This universal intelligence is what we call God. Call it by any other name, it is absolutely certain that in the beginning there is that Infinite cosmic intelligence. This cosmic intelligence gets involved, and it manifests, evolves itself, until it becomes the perfect man, the "Christ-man," the "Buddha-man." Then it goes back to its own source. That is why all the scriptures say, "In Him we live and move and have our being." That is why all the scriptures preach that we come from God and go back to God. Do not be frightened by theological terms; if terms frighten you, you are not fit to be philosophers.This cosmic intelligence is what the theologians call God.
The evolution of beings was first presented to the world by Patanjali in his Yoga Aphorisms (IV. 2-3) (available here under the heading Raja Yoga, sub-heading Patanjali's Yoga Aphorisms, sub-sub-heading Independence http://cwsv.belurmath.org/volume_1/vol_1_frame.htm). It is all one Atman, It is the One apparently appearing as many, there is only an apparent evolution- an apparent involution and evolution.