Laser Hair Removal
First we should address that laser hair removal isn't "permanent" but it is "hair reduction" when the recommended 6-8 treatment protocol is followed. Our office does these treatments 4-6 wks apart and has great success. It is possible the hair you are seeing now was in a resting state when you were treated 3 months ago and it is now active.
Laser Hair on Face
Laser hair therapy works extremely well. I wish you had given more information like what laser you had done or a photo of your skin. It sounds like you need additional laser hair treatments to correct the problem. The other problem may be that you have dark hair/skin and need a different laser completely to finish the process. Please find a board certified dermatologist in your area who has experience with lasers for the best cosmetic result.
Laser hair removal and facial growth
If it is pigmented hair, it may be that your hair was in a resting phase and has now started to grow. If it is dark hair, it should actually respond very well to laser hair treatments. Faster growing hair is more effectively treated than slower growing hair. It also may take 6 to 8 treatments on the face to slow or retard hair growth on the face so I would continue with your treatments.