When I read kavachams, sahasranamamas and ashtothrams, there is mention of anga nyasa and kara nyasa.
I am yet to be initiated into gayathri.
Can I do anga and kara nyasa?
As you may be knowing that during Anga/Kara Nyasas Mantras like Om, Swaha, Vashat, Vaushat, Bhurbhuvasuvar (which has portions of the Gayatri Mantra) etc should be recited.
But, according to scriptures, uninitiated persons (in your case without Upanayana) should not chant any of those Mantras. Actually, the only Mantra he is allowed to chant is Swadha which is used during funeral rites.
Manu smriti 2.172. (He who has not been initiated) should not pronounce (any) Vedic text excepting (those required for) the performance of funeral rites, since he is on a level with a Sudra before his birth from the Veda.
Similarly, the Baudhayana Dharma Sutras 1.3.6 also states the thing:
6 Before the cord of Muñja grass is tied, they do not impose any ritual observances on a child, for until he is born through the Veda, he is equal to a Sudra in conduct.
So, one should not and wait till the initiation is complete. As, there is scriptural prohibition.