As with many questions, on this particular question you will get different answers, and sometimes even contradictory answers, because different Hindu traditions (sampradayas) have different explanations of those things in their systems of Vedanta. Those who follow dualistic systems of Vedanta, such as those of Vaishnavas, will say that there are two souls (atmas) in the body of each living being, namely Supersoul (paramatma) and individual self or jiva soul (jivatma). So the answer to your question is that of those two souls in our body we are only jivatma soul, but we are not the other soul called paramatma.
Vaishnava conclusion is that the individual living entity (jivatma) is eternally different from the Supreme Soul or Supersoul (paramatma) who exists as Supreme God:
dvā suparṇā sayujā sakhāyā samānaṃ vṛkṣaṃ pariṣasvajāte tayor anyaḥ
pippalaṃ svādv atty anaśnann anyo abhicākaśīti
"The individual spirit-soul (jivatma) and the Supersoul (paramatma), are
like two friendly birds sitting on the same tree (body). One of the
birds (the individual atomic jiva soul or jivatma) is eating the fruit of the
tree (the sense-gratification afforded to the material body), and the
other bird (the Supersoul or paramatma) is not trying to eat these
fruits, but is simply watching His friend (jivatma)." (Svetasvatara Upanishad
Here it is clearly pronounced the difference: "two friendly birds" and also "the other bird"!
Sanskrit: dvā suparṇā -- two birds; anyaḥ -- the other.
Two birds (two souls) are never just one bird (ie they are never one and the same soul!), and also the verse clearly says "the other bird"! which means that the verse is also talking about the other soul and not just about one soul. Thus, the difference between the two souls is established in this verse of the Svetasvatara Upanishad 4.6.
According to the Vaishnavas this difference between the two souls, jiva and paramatma, cannot be denied. This difference is real and eternal.
The same is also stated in the Mundaka Upanishad 3.1.1:
"Two birds, inseparable friends, cling to the same tree. One of them
eats the sweet fruit, the other looks on without eating."
In those verses we also see that one bird (jivatma) is eating the consequences of karma "one of them eats" says the verse, while the other bird (paramatma) is not participating in karmic results because the verses say "the other looks on without eating". From this we also see that there is the difference between the two souls because it would be absurd to explain those verses that they teach about only one soul, namely it would be absurd to think that one and the same soul simultaneously is affected by karma and is not affected by karma. The only logical explanation is that two different souls exist in the body, one is subject to karma, and the other is not subject to karma. Obviously we are not that other soul (paramatma) who is not subject to karma.
You are just the jivatma. You are not the heart, mind, feelings, consciousness, senses and body. You are not the paramatma as well. You are the witness of your individual feelings, thoughts and body. You are the jivatma who is feeling, thinking, can see and hear, etc. But all that you can do only connected with your own body. You can not witness the feelings, thoughts, and bodies of other living beings. But paramatma can do even that, he can witness everything, all the bodies, all the thoughts, etc, of all the living beings.
Jivatma is situated only in one body, namely in his own body, but paramatma is situated in all the bodies of all the living beings.
Here is the verse about one God who is paramatma dwelling in all beings, all-pervading Lord who is the witness watching over all the jivas or living beings (jivatmas) and watching over all their works or activities (karma):
eko devaḥ sarva-bhūteṣu gūḍhaḥ sarva-vyāpī sarva-bhūtāntarātmā
karmādhyakṣaḥ sarva-bhūtādhivāsaḥ sākṣī cetā kevalo nirguṇaś ca
"He is the one God, hidden in all beings, all-pervading, the self
within all beings, watching over all works, dwelling in all beings,
the witness, the perceiver, the only one, free from qualities."
(Svetasvatara Upanishad 6.11)
Thus we know that paramatma is dwelling in all beings, and thus He is witnessing and watching over all the jivatmas. Thus He is the witness of everything, ie of all the bodies, all the thoughts, deeds, etc, of all the living beings.