Not long — and the pain stopping is not the good sign it feels like.
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A dental abscess does not resolve by itself. It is a pocket of infection with nowhere to drain, and the only real fix is removing the source — a root canal or an extraction. Antibiotics can hold it back for a few days but they do not cure it, which is why an abscess "treated" with antibiotics alone almost always returns. Get seen within a day or two. Go to the emergency room the same hour if swelling is spreading toward your eye or down your neck, or if you are having any difficulty breathing or swallowing.
A tooth abscesses because the nerve inside has died. While it is dying it hurts badly. Once it is dead, the pain often stops for days or even weeks — and almost everyone reads that as the problem going away. It has not. The infection is still there, and now it is spreading into the bone around the root with nothing to warn you. Sudden relief after severe toothache is a reason to be seen, not a reason to cancel.
If any of these apply, go to the nearest emergency room or call 911. That is a hospital problem, not a dental one.
They will knock it back and buy time, but they do not fix it. The infection is fed by a dead nerve inside the tooth, and antibiotics do not reach there — that is why it returns once the course finishes. The tooth needs a root canal or removing.
It can. Infections in the lower jaw can spread into the floor of the mouth and the neck, and in the upper jaw toward the eye. Those are rare but genuinely serious, which is why swelling that is spreading, difficulty swallowing or trouble breathing mean the emergency room, straight away.
No. Squeezing or lancing it pushes bacteria deeper into the tissue and turns a contained problem into a spreading one. Warm salt water rinses are safe and help. Anything sharper does not.