Have a crossbite and do not want surgery, I need some advice? (photos)

You have a pathologically under-developed maxilla.  Orthodontic expansion addresses the teeth and you need orthopedic expansion.   The process requires wearing the DNA Appliance 14-16 ours/day but has minimal discomfort.  Rapid Maxillary expansion with a surgical assist is an alternative (SARPE) but Epigenetic Orthopedics give better 3 dimensional expansion which has advantages.

Crossbites like yours come from an upper jaw that is to narrow, OR a lower jaw that is longer on one side than the other, OR some combination of the two.  The only way to expand adults is with an MSE appliance if indeed the problem a narrow upper.  (Expansion of the upper with any appliance just pushes the teeth out of the bone.)  Asysmeteric lower jaws require surgery (sorry).  The worst possible thing to do is to try and treat this with traditional braces alone.  An orthodontic evaluation from a specialist will answer your questions.