This sounds exactly like what my daughter suffered from beginning at 7 months. She was born in 1979 and no one ever diagnosed her either. We always knew she was going to be sick every 4 weeks to the day and adjusted our family schedule to revolve around her illness. She was on Phenobarbital  for a year to prevent seizures, which fortunately she never had although her fevers ranged from 105-108. She also spent a year on Prednisone which didn't help. Although we went to St. Christophers  Hosptial in Philadelphia and AI Nemours in Wilmington, DE  for years, we never got a diagnosis. After missing  a lot of school (5-7 days a month), and spending once a month in the hospital because she would get so dehydrated, it was suggested that we have her tonsils and adenoids removed. She was in third grade and woke up like a  different child. Although she still had fevers, they were not as high and not every 4 weeks anymore.
She is an adult now and still gets fevers, joint pain and sore throats often but not every month.
I never heard of anyone else that had these symptoms until I looked them up recently and heard about PFAPA. It feels great to be able to finally put a name to this chronic illness.