The healing process depends on how long it takes for all the rubbish to come out and how deep the abscess is.
If the root of the abscess is left, it will continue to fester.
Make sure that you take the antibiotics as prescribed and do as the doctor advised you.
Take pain relief medication as prescribed on the packet to help lessen the pain.
I'm sorry to hear of everything you are going through. The pain should subside as the pus/drainage comes out. Even though the doctor opened it up, the goal is to encourage it to keep draining to get the infection out of your body.
It probably will remain swollen for several days, but everyone is different, so no one can say for sure how long this will be.
Antibiotics take at least 24 - 48 hours before they start working. Follow the directions closely as many interact with foods and other medications. Also make sure you finish them even if you start to feel better.
Since you were not prescribed pain medication, if you feel that taking over the counter pain medication if not enough, contact your doctor if you need something stronger prior to your next appointment with her.
If your drainage goes through the dressing she put on you and you are unable to change it on your own, either apply more gauze to the area and tape it, or contact her office to have her change it sooner.