Many MDs will treat post-fraxel hyperpigmentation with broad spectrum daily sunblock, hydroquinone 4% gel and one percent hydrocortisone & perhaps a retinoid. Melasma is very difficult to treat. I would be optimistic and go back to a dermatologist and slowly try to lighten them up with topicals. If you no longer trust the Fraxel, sometimes regular, light, Beta-Lift peels can be helpful as well. Avoid the sun and always wear broad-spectrum SPF. If you drive a lot, put UV guards on your car windows. If you are light skinned, sometimes TCA localised peels can help.
So go back to your dermatologist and come up with a plan. The Fraxel 1550 often has a specific melasma setting that works well if you use a bleaching agent for a month prior to using the melasma 1550 setting on the Fraxel. There is always hope & always a way for some improvement. Sometimes it helps to give the skin a long rest before trying something new. Best of luck to you.