Thanks for the query..
You symptoms of having episodes of severe pain
is pointing towards nerve related pain and most probably it is Trigeminal Neuralgia
as it is the nerve of face and your symptoms are very much consistent with it..
Although you have a decayed tooth and it might also be painful but this episodic pain is appearing to be due to trigeminal neuralgia only..
Your CD4 counts are considerable as of now you need not to worry about HIV relating to this..
You should consult an Oral Physician and get your broken tooth examined with the help of x ray..
If it is broken vertically then it might need extraction or else Root Canal treatment
and capping can save the tooth.
For this episodic pain if it does not subside with treatment of tooth then you should see a Neurophysician as they can advise you MRI scan and if neuralgia is diagnosed he can advise you neurotic painkillers that commonly help with such pain like Carbamazipine [Tegretol] , Oxycarbazipine [Trileptal] and Gabapentin
For now you can take painkillers like Ibuprofen
[Advil] but if pain is severe Tramadol [Ultram] can be taken for relief..
Hope this helps..