I had an abscess drained yesterday and the dentist gave me antibiotics. still, my tooth is very swollen. will theswelling go away soon?

Hopefully soon: It often takes at least a couple of days, sometimes more for this to start resolving. If in doubt, call your dentist and ask your questions or to be seen if necessary. If it gets worse, you have a fever or other worsening symptoms, call your dentist immediately!

Takes a day or two: The antibiotic works when the bacteria are dividing, and since they don't all divide at the same time, it can take a few days. This should be monitored very closely by your dentist... It is very possible that the antibiotic needs to be changed if it is not working. Let your current dentist know what is happening.

Maybe: Although draining an abscess and antibiotics are very important in decreasing the swelling you must not forget that we also need to treat the source of infection as well. Whether you have to get a root canal or an extraction, then make sure you get it done or your swelling will come back.

It should: Yes, since the dentist gave a place for the infection to drain, the swelling will go down. Make sure to take all the antibiotics too. Ultimately though, you must get rid of the source of the infection, the bad nerve in the tooth, if you want to totally get rid of it.