Hi Jaynea,
To most dentists, a diagnosis of a "tooth root infection" is meaningless and at best, ambiguous.
A tooth with an endodontic infection (infected nerve), a periodontal infection (infection of the gum and bone around a tooth or infection of a tooth associated with a fractured root (the bacteria cause an infection by penetrating the root and then either affecting the surrounding bone below the outer surface of the bone or the nerve within the tooth.
In all of these cases, the root is in close proximity to the "root". Better diagnoses would be a periapical abscess, periodontal abscess, pericoronitis, endodontic abscess, acute or chronic apical periodontitis, etc.
I suspect (but cannot be sure) that your dentist was diagnosing some sort of periodontal or gum infection that was within a pocket that had formed next to a tooth root.
If you have a simple, soft tissue infection with no bony involvement, an antibiotic may actually solve the problem. If it returns, you have to look further into the etiology of the problem.
While an antibiotic may resolve the problem temporarily, if it involves the underlying bone, it almost always will return. Typically, the dentist will also scale and/or root plane the affected area. He may apply some topical antimicrobials and Rx an antibiotic.
Often, if there is one area of periodontal disease in a person's mouth there is likely other places...not always...but usually. Treatment consists of a thorough debridment, root planing, re-evaluation and possible surgery to eliminate pockets.
Now, on the other hand, of you had an abscessed nerve within the tooth, then the only sure treatments are root canal therapy or extraction. An antibiotic may temporarily stop the infection and pain but it is guaranteed to return. Usually, in days or weeks but on rare occasion, months to years. The longer you take to recieve definative treatment, the poorer the prognosis.
A fractured tooth can allow bacteria to enter the tooth's nerve area, the surrounding bone or both. Not all fractures can be seen in the mouth AND THEY ALMOST NEVER ARE REVEALED ON AN X-RAY! Some fractures can produce endodontic abscesses, other may cause pocketing and a periodontal infection.
Either periodontal or periapical infection can have diving implication...although of low probability. Unfortunately you cannot tell who will be affected so treatment is the best option...before diving.
I'm hoping that you dentist is, indeed correct. If you problem was soft tissue only and if it clears up with the antibiotic, you may be able to dive. If you have any problems during the dive, signal your divemaster/instructor and discontinue the dive and don't dive again until the problem is resolved. Why not contact him one more time and find out if there is a minor gum problem, a major gum problem or a root canal problem.
Hope this helps.
Laurence Stein, DDS