I closed on my very first house November 23rd of 2015 . I did not claim the mortgage points on 2015 taxes can I do that for 2016 tax purposes?

Sorry, but points are only deductible in the year paid.  You would have to amend your 2015 return.

Even if I didn't make a payment until jan1st?

Points are deductible when paid.  If paid at closing, either from your purchase money deposit or signing the mortgage, it was paid in the year of closing.