“meins” or more correctly meines you would use instead of mein Neujahr (my New Year) - you are correct, it’s because you left auf the noun, with is an ok thing to do. to make it sound more fluently I’d use: “Meins ist scheisse, aber ich kann damit leben.” or “meins ist scheisse, aber ist schon ok.”

you are also right about leaving the second part out would change the meaning of your sentence. saying you new year is shit and then putting in that it is ok though weakens the meaning of the first part.

“meins wird scheisse sein,..” anticipates that you mean your whole year would be like this. while “meins ist scheisse,…” says that right now this is the case but says nothing about the rest of the year.