Fraxel left me squares after one month will this fade over time?

I'm so sorry your healing process hasn't been a smooth transition. It is never recommended to remove scabs or flaking after having a procedure because this can create scar tissue. If your skin is discolored in a pattern, you may want to try Melamin and Melamix-with Retin-a for 4 weeks to blend the pigment together. Your healing process can take any where from 28-40 days due to skin cell turnover. Cell turnover is the skin's natural exfoliation process. The skin naturally sheds deadskin cells through a process called desquamation. Every 28-40 days, on average, a new skin cell is "born" in the stratum germinativum, the deepest layer of the epidermis.I hope this helps. Be well. 

After one month the effect of the Fraxel should have dissipated. The Fraxel laser does not leave "squares" behind as it is a roller and not that type of handpiece.  I suggest you consult a board certified dermatologist to see what kind of laser was used and evaluate your healing.  Best, Dr. Green