My social security is being taxes in two states rather than pro-rated after I moved

I can't be too specific without knowing what states you are dealing with, but in general the states tax all of your income no matter where it is earned, and then your resident state will give you a credit for taxes paid in the non-resident state. You need to look for a credit for taxes paid to another state on your resident state return.

If you moved during the year (changed your permanent residence), you are a part-year resident of each state.  You must allocate each item of income to the state where you are living when it was paid.  

You should not be filing a full year resident for one state and a non-resident for the other state.