It's correct except for "του γιούς μου". The genitive case is "του γιου" and no accent mark is needed because it is an one-syllable word. (don't be confused by the fact that there are two vowels, the word is pronounced as /ʝɔs/.) So, Ο Ιούλιος είναι ο μήνας του γιου μου. ;)
Thanks so much for the response! This makes perfect sense.
For some reason, I got confused and thought that all possessives were formed using the genitive, but now I see that the genitive is only used for constructions meaning "of the possessor" or "the possessor's noun".
In the case of the "my/your/his/her" construction, it seems that the pronoun is already in the genitive (i.e. μου is a genitive declension of εγώ etc.). Is this correct?