3 months after Fraxel Laser, I have dots & lines on my face, will this heal or is it permanent?

First, let me say that I am sorry that you are having this difficulty. Unfortunately, to date I have found the results of of many of the light-based devices, including IPLs and fraxels, to be supported by a whole lot more manufacturer-based marketing hype than hard science. That having been said, three months seems like a prolonged period of healing,  and I would agree that it would be important to return for follow-up to the treating physician. Medical microneedling therapy, using either the manual Dermaroller or the automatic Dermapen, both of which are used for treating irregular skin texture and blotchy pigmentation, would be an option to consider for dealing with this problem should it come to that. I have been performing skin needling of both kinds for about fifteen years with gratifying results for these kinds of issues. Usually a series of two four treatment sessions are required for optimal results, but fortunately these treatments are accompanied by little downtime and most people can return to normal activities the following day.  I recommend that you search the archives of Realself.com for more information and details on this approach.

Fraxel is a great laser for pigmentation and scars.  It is unclear which setting you had and for which indication.  If you still have marks three months later I would recommend you return to your treating physician for examination. 

The Fraxel re:pair laser may temporarily leave small visible dots on oily skin where the healing of the laser holes is inhibited by the oil in the skin.  In most cases these dots will disappear within a few months without treatment. As for lines and stripes, check back with your doctor.  It may be necessary to do a blending peel to make the skin even.