First off your spherical equivalent would be -7.75 right eye and -6.50 left eye. LASIK candidacy would ultimately be dependant on your corneal thickness and curveature. Is there enoug tissue to treat? Is your cornea steep enough to treat?
Surface treatments such as PRK or LASEK would preserve more corneal treatment. There is a slower healing process, but if done with mitomycin c (MMC) would have minimal haze risk.
LASIK would provide a faster recovery but carries the flap complications.
The accompanying video will explain the anatomical differences between the procedures.
A final option would be the ICL, an implantable lens to improve vision.
I think the most important thing you can do is to seek the advice of a refractive surgeon who is well versed in all refractive techniques. It doesn't sound like this has been the case thus far.
Good luck!