Do i have to get my tooth extracted after a gum abscess?

Not always: If the bone loss is not too advanced it is treatable and savable.

Maybe: If the abscess is caused by a root fracture, extraction is likely. If the abscess is caused by tartar under the gum line, it can probably be treated by a periodontist to save the tooth, unless the bone loss is severe.

Usually no: Acute abscess usually are reversible in term of bone loss. However, chronic abscess may result in severe bone loss of which the bone graft is unpredictable. If the tooth exhibit a class iii mobility (moving back and forth more than 2mm and depressible into the socket), the tooth has loss most or all of the bony support and should be extracted. Otherwise, treat the cause and the occlusion.

It depends: The best chance of saving your tooth is by getting the abcess treated ASAP so you can restore the area to good health. If there has been severe destruction of the bone then extraction may be needed.