Yeah, they are quite painful. When I shattered one of my wisdom teeth I thought it was tooth ache but it turned out to be an absess that needed treating first.
As said it can take a couple of days for the antibiotics to stop it's gallop and then each day will be a big relief. The salt water washes are a good idea to help clear the area and something the medical profession use a lot for cleaning (that's all saline solution is). I do these every time I have a throat problem with a cold. It helps break up any mucus too.
Now you have another reason why a pair of pliers would have been a bad idea. Bursting an absess into your mouth and a likely throat infection (and probably puking up your tea as the stuff reeks) wouldn't have been a good idea. You might find your mouth stinks a bit and that's the absess.
Really not much you can other thna recommended and wait it out. When my antiobiotics ran out I noticed the pain coming back a few days later and this was because they hadn't killed it off completely. It just meant another course and it was nowhere near as bad as the original anyway. So, if that happens just head back to the dentist for another prescription if needed.