I am a non NY state resident. Turbo Tax will not allow me to put in what I made while I was in NY State nor the NY state income tax

You need to revisit the NY allocation screens.  On those screens, towards the beginning of the NY nonresident interview, you have the opportunity to enter the amount of income you actually earned in NY, either by stating the exact amount, or by prorating the amount of income by the percentage of days worked in NY.