Are there eye contacts that are totally cosmetic to make the cornea whiter but keep my iris/pupil color?

Conjunctiva? . The cornea covers the pupil and iris. It is clear. You must mean the bulbar conjunctiva. This is the "white" part of the eye. Contacts don't extend out to the conjunctiva so they can't change its tone.
Special eye contacts. I don't know of such a thing.