Once a person has infection with either HSV type, it is rare for that person to become reinfected with the same type, either through auto-inoculation (e.g., transmission of genital infection to the mouth or eye) or by exposure to a person with the same virus type. On that basis alone, it is unlikely that your throat symptoms are due to HSV-2. When herpes infects the throat, it generally does not cause visible blisters, only open sores; and most apparently "blisters" inside the throat are actually just edema (swelling) of the mucous membrane or perhaps lymphoid follicles just under the surface. The cycle of symptoms you describe does not suggest herpes; just as with your recurrent genital herpes, herpes would cause symptoms for a few days at a time, followed by much longer periods with no symptoms whatsoever. Finally, although first-episode herpes of the mouth and throat often causes sore throat or sores inside the mouth, recurrent oral herpes almost always is external, on the lips etc.
So both the overall sequence and your symptoms make herpes a very long shot and I very much doubt that's what's going on. I share your implied criticism of your doctor for not doing culture tests for HSV. But the odds are it didn't actually miss anything. Anyway, if your symptoms persist, see your health care provider (or find another one, if you lack confidence in the previous guy). But herpes isn't going to be the explanation.
Good luck-- HHH, MD