The usual reason for an air valve to stick is contamination. You'll probably have to take it apart and clean it. If you do, be careful not to lose any of the really tiny parts. There is most likely a little rubber O-ring. If you got lacquer thinner on it, it can swell and stick. Just let it dry out a couple of days. If there is paint in the valve assembly, you probably have a leaky needle bearing or else you pulled the needle while there was paint in the cup. Some people put airbrush lube on the valve parts. I don't, but it couldn't hurt. You might get more specific help if you mention which airbrush you have.
Don