Can active FX laser cause permanent swelling? I had procedure done a month ago and still have some swelling on upper cheekbones

With laser resurfacing of the sort you underwent there should be some residual swelling at this stage. Ultimately, within a few months or maybe more, that swelling will resolve. The wound created by the laser is really quite broad in terms of surface area. All wounds heal by the same wound healing process that includes inflammation and remodeling. That process progresses for months if not a year or two. The swelling you and others can actually "see" will resolve over ~ 3 months. Hope this helps.Best of luck. 

It is normal to still have some swelling a month after laser therapy.  You also could have some residual redness.  I would expect you to see your final result at about 3 months.f