What specialty should I be looking for in a doctor to surgically remove permanent fillers from nasolabial area?

I'm truly sorry that you are having this problem. I have been cautioning my regular followers for many years now that permanent fillers can translate into permanent problems, such as nodules, granulomas, thickening and stiffening of the skin, etc., not only shortly after treatment, but even five, ten or twenty+ years later. And Unlike, natural fillers, such as HA fillers, for which there is an enzyme, hyaluronidase, to dissolve them, permanent fillers, which are essentially foreign bodies that stimulate fibrosis to wall them off, they do not have any dissolving enzymes. So sorry. That being said, I have personally had gratifying results in treating persons who have been treated elsewhere with permanent fillers, such as Bellafill, using an algorithm of varying combinations of anti-inflammatory agents in varying concentrations and amounts. Make sure to consult with an experienced, board certified cosmetic dermatologist and best of luck.