You could just request the transfer, without a reason. If the manager wants a reason, then tell them that after your car was stolen you don't feel safe in that area. I don't see any reason they need to know about the PTSD or anxiety, personally.

You could also state that you didn't feel like your coworkers connected or cared at all, and that you would be more comfortable in a store where there is support of some type. That one could be a little more risky, tho.

I always lean toward not disclosing mental illness or health info unless absolutely necessary. I live in a state, however, where they can fire a person for no real reason, and unless you can prove discrimination beyond doubt, there's nothing that can be done. That makes it a little more difficult here.

When I was working at a large warehouse type store, there was a day, during construction on the bathrooms, where they were going to be testing the fire alarm several times. We were warned ahead of time that they would be testing throughout the day, and I pulled my team lead aside, and just told her that I don't handle extremely loud noises well. They were also going to be announcing a few minutes prior to the test for the customers, because no one needed to evacuate during the tests. I told my lead that I would need to step outside when the alarm was going off, which would be for 5 to 10 minutes, and happened about 4 times during my shift. She did ask what would happen if I had to stay inside during ther alarms, and I told her I would be unable to work duri my the alarm and for a time after while I composed myself again. I never used the term PTSD, but I also didn't say it wasn't. I left it open for her to think what she wanted, but I did not verify anything. She did allow me to step outside during the alarms.

Basically, there are ways to explain things without giving too much info, because in my opinion, it is hard to tell when someone will use that info against us.