Had a misdemeanor arrest when I was 17. It will show up on FBI check.

I was innocent and the charges will also show up dismissed. Will this stop me from obtaining residency?

Are you sure it will show up? I, too, was arrested on a misdemeanor charge and found not guilty at trial, in addition to earlier arrests for driving while suspended. Still, my FBI certificate says "No Arrest Record".

My understanding is that if an arrest shows up on your FBI report, it will only show the arrest and not the disposition of the case. I could be wrong about that.