What would be the difference between synonymic and synonymous? If there isn't any,is it synonymic to/with?
If you are going to use the word (which the OED suggests is not synonymous with 'synonymous'), people are more likely to think that the word itself is a mistake than to worry about the preposition you use.
Webster's 1913 dictionary gives synonymic a distinct meaning as a noun:
Webster's Revised Unabridged Dictionary (1913) - The ARTFL ProjectSyn`o*nym"ic (?), n. [Cf. G. synonymik. See Synonymous.] (Gram.) The science, or the scientific treatment, of synonymous words.
I have to say that I had never bumped into the word before.
I had never heard it before either. If I were you, I would keep using "synonymous" in class with the teacher. If the teacher pulls you up on it and asks why you're not using "synonymic" as he/she does, you can always tell him/her about this website and the fact that plenty of native speakers have told you that it's not used in everyday language and was completely new to several of us.