I've gotten a bunch of xrays in the past 3 months from my orthodontist (cephalograms) and from the doctor removing my wisdom teeth (dental x rays). Could this cause permanent hair loss or other side effects?

No. You would need to be exposed to very, very high levels of radiation to experience any permanent changes.
Absolutely not. The totality of the radiation you received for Orthodontic Records and Wisdom Tooth Evaluation is less than normal background radiation on one transcontinental flight, or a day in the mountains, or two days on the beach. So next time cut your vacation short by a day to make up for it. Andy the way, call a Dermatologist now for an appointment to discuss your hair loss.