I moved to a different county and have to update my voting information. Would I still be able to vote?

I’m admittedly sort of uninformed when it comes to voting since this would only be my second time doing so. But I moved from Harris County to Montgomery County a few weeks ago and realized I have to re-register to vote because of my new information. I should have done this a while back and it’s my fault.

Will I still be able to vote or am I screwed?