If you are not on the books at the polling place of your new district, you can vote by provisional ballot and they will have you provide proof of new residence, after which your vote can be counted. (They'll give you a slip with a number to call in 7-10 days to check your ballot's status)

I myself just had to vote provisionally for a similar reason. Don't let a clerical error deprive you of your right.

Sidenote: to answer your question: yes. If you are still registered to your previous adress, your name will still be on the books for that district and you will be able to vote there. Technically, the provisional route is the correct way, since you would be voting for local representatives of your previous adress, but in reality you would have no issue if you were to go there.