Have does had a abcess drain at the dentist yesterday how long does it take for the swelling of my top lip take to go down?

Shortly...: I would expect that swelling to decrease appreciably within a few days. If this does not happen i would contact the dentist for an evaluation to make sure things are not getting worse.

2 to 3 days: What else was done or scheduled. If there is a cause for the infection needing drainage, that cause has to be addressed.

A few days: You are probably taking antibiotics and the swelling should go down with in a few days.