My question to you would be do you have function in your right leg and are you able to walk on it? If so, I'd be concerned that freezing then burning those nerves may make you have less function in that leg provided which exact nerves they are,I suppose. Of course, you want no or even less pain, but I'm sure not at the cost of function.
I'll be watching this thread with interest as I often have significant pain in my left hip and mid back and have been thinking about seeking out a pain specialist and wondered in advance what options they might give me.