Periodontal Abscesses almost always happen in people who have existing periodontal disease that is advanced enough to have resulted in some loss of bone around the root of the tooth.  An area in which bone is missing around a tooth root is called a periodontal pocket,  and a periodontal pocket can be very hard to clean.  The bacteria living in the pocket change and, over time,  more destructive species move in.  Byproducts of the bacteria cause more bone to dissolve.
Periodontal infection can be present without pain, but, if there is pus forming, and is it trapped under the gum,  this periodontal abscess pain can be quite bad.  The infection can spread and seem like it is going into your ear or under your lower jaw and down into your neck.  It may be hard to open your mouth because of the inflammation and swelling. (See my Periodontal Disease site for more information.)

First, a dentist will need to diagnose the problem. The dentist will need you to explain how long you have been in pain, how severe that pain is and what the quality of that pain is (sharp, with cold, with hot, with chewing, constant,  intermittent, annoying,  "pretty bad" or "so bad you can think of nothing else"). Also,  you will be asked if you can you pinpoint a specific tooth, area, top bottom, etc. A dentist will also try to ascertain the history of the teeth in the area,  other problems or treatments that have occurred there. A tooth need not be dead to have a periodontal abscess so the tooth may still feel cold.
      An oral exam will reveal any swelling, whether any teeth hurt when tapped, whether suspect teeth are loose.   An X-ray will possibly show the presence of periodontal pocketing.  The depth and location of pockets  (in millimeters) will be checked with a periodontal probe.  Sometimes, an obvious bubble-type swelling is seen around the tooth.  When this area is probed,  pus and blood can drain out.  This is common in periodontal abscesses.  A patient may notice that if he or she pushes on the gum around the tooth, it hurts.  Sometimes it bursts, pus drains and there is some relief.
      If your problem seems to be a periodontal abscess,  the dentist will probably place you on an antibiotic (amoxicillin 500 mg 4 times a day for 10 days.  Erythromycin will be used if you are allergic to the penicillin family). The gum area will be cleaned out a bit, debris removed and the pus allowed to drain.  You should start to feel better relatively quickly but it is important to realize that there was an underlying periodontal problem that needs to be addressed.

At times, a tooth may have a periapical abscess and a periodontal abscess.  This is called a "combined" lesion. Both problems need to be treated and the  prognosis of the tooth may be guarded.  Maybe it can be saved. Maybe you will need an extraction, followed by a  bridge or implant. (See Dental Crowns and Dental Implants for more information.)