This question is missing a few details like whether the tooth was removed or not and what if any treatment was recommended after the antibiotics were gone.
Hi there, Bone fragments can work their way through the gum after a tooth is extracted but it seems more likely that part of your tooth is still there.
Did you have the tooth extracted after it broke or did you just take antibiotics?
Teeth that break don't normally break with a clean and smooth edge....broken teeth can have a sharp jagged edge.
Either way, you need to see a dentist. Antibiotics that are prescribed for a tooth abscess often are not the whole solution. It is common to need further treatment after the antibiotics are taken. Tooth extraction or root canal therapy is likely to be recommended.
If you still have part of the tooth, it may be possible to repair it with a filling or crown.
Or if too much tooth is gone... which is likely if it broke at the gum line....you need to have the rest of the tooth removed so your gum can heal completely. Your lip will feel better too.
If you already had the tooth extracted it could be a bone fragment and your dentist could remove it.
If you end up losing the tooth, a dental implant is the best way to have it replaced.
Thanks for writing and good luck,