I know this is an old thread, but someone always has a tooth ache, so old is new.

My remedy for an abcess is tried and true. Put ice in a paper towel so it doesn't stick to you, and hold it on your face next to the bad tooth inside your mouth. Do this as long as you can stand it. The first round of ice is to numb the gums around the tooth.

Sterilize a pin, any kind of pin, safety pin, needle, whatever. Then, pull the lip outward, and find the reddest spot - there might be a small white or yellow spot there.
If the white spot is showing, poke it with the pin. If it isn't, find the worst of the red where it is swollen, and prick it with the pin.

Now, back to ice on the face as long as you can stand it.
Keep checking the abcessed spot after the ice melts.

It may take a few rounds of ice, and a couple of pricks at the spot with the pin, but the abcess will become blister like on the gum. Pop it, use a q-tip to squeeze out the infection.
You are golden at this point. Over the course of a day or so, you will still need to push the infection out, but there should be very little left.

Your gum will be sore. But the abcess will be gone.