"I 've done nothing to you" I will say that main I haven't do anything to you now, it is present time now. "I did not do anything to you" I would say in the past I did not do anything to you at all.

the first sentence is correct. the second sentence is a double negative potentially. you should use the first even though you will the hear the second sentence. It is not recommended. and never say this"I didn't do nothing" <this is a double negative