This type of pain can be excruciating or dull. It is caused by the death of and subsequent infection of the nerve and other tissue in the space that occupied by the nerve (the pulp). 
Symptoms include:
- Pain when the tooth is pushed  or tapped on;
- Pain when biting (and the pain does not disappear immediately after opening); No pain with cold; cold may feel good (The tooth does not hurt when you put an ice cube on it; it's dead and can't feel cold; the pain of an abscess comes from inflammation around the root);
- Sometimes a little bubble on the gum near the root of the tooth (This "fistula" is a tunnel your body has made so the pus can drip out. If a fistula forms, the pain may improve, but you still need treatment).

The Treatment for Tooth Abscess:
Treatment possibilities are
- No treatment, which is life potentially threatening.
- Extraction of the infected tooth;
- Root Canal
- Antibiotics. The right antibiotic will reduce the inflammation and help the pain but the tooth still needs definitive treatment. Otherwise the infection will continue to recur.  (What antibiotic works?  Amoxicillin (if you are not allergic to the penicillins), are the first line of defense.  (500 mg 4 times a day for 7-10 days).  A small percentage of tooth abscesses do not respond to Amoxicillin  (or the cephlexins) and require Clindamycin.  See a dentist for the right Rx. Or go to an oral surgeon, an endodontist or even an ER. (Physicians don't always know about Clindamycin. The hospital oral surgeon or infectious disease person will, though.)  If you have any drug allergy, tell the doc.

When traveling in remote places in Asia I have noticed that people often assume the antibiotic they use for G.I. Infections (Usually Ciprofloxin or its progeny) will work. It won't.  An abscess is potentially life threatening.

Please remember that this information on this site is not all-inclusive and it may or may not apply to your situation. You need to call your own dentist.  A dentist needs to see the tooth, take and x-ray, etc. to diagnose and treat.