In my experience, the desensitization process was geared toward the allodynia, increasing tolerance for things touching your skin in the affected areas.

If you are ready to cry from muscle spasms, it sounds like your problem is "deeper" than the skin issues. Going through desensitization will normally cause DISCOMFORT to the skin. If that pain is too severe, in my opinion, the pain should be better managed BEFORE getting aggressive with desensitization techniques. If this process is causing deeper pain and burning to your muscles/main RSD site, it sounds like this therapist is overdoing it with you.

Pushing through discomfort = reasonable. It's what we all have to do to get out of bed and get moving each day.

Pushing through pain = BAD !!!!! For me, that's just asking for days of markedly worse pain after a massive inflammatory response.