Try Gabapentin and see if that works better for you than Lyrica. PT is hugely important, but you won't notice a change immediately. You need to do desensitization for the burning sensations, which can mean just stroking with a cotton ball gently for 20 seconds at a time, never letting it get to the point of triggering the burning. And just doing that maybe 10 times, whatever you can manage. But then doing that several times during the day. Dipping it in room temp water. OR cool water. In and out.

There are some anti-depressants that also work on nerve pain, so if Lyrica/Gabapentin make you too foggy, that may be another option. But don't give up entirely on Lyrica/Gabapentin, sometimes you just need some time to acclimate and won't be so foggy.

Nerve blocks are one of the standard early treatments used to try to stop RSD/CRPS. Since mine is in my foot it was a lumbar block, not sure how they do it for arm/hand.