What would be the difference between synonymic and synonymous? If there isn't any,is it synonymic to/with?
No examples of sentences containing the word are to be found in the BNC, and only one each (as an attributive adjective) in COCA and Webster's 3. The five citations in the OED contain the word used only as an attributive adjective.
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.
Context is always important; labelling is rarely important.
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.