Personally I prefer a longer acting medication, if you can get ahead of pain it is more effective than chasing it all day. I know that prescribing opioids is now a big deal and many docs are very conservative about it.
My first pain doc went to Methadone because it works on different receptors in the brain, which are thought to be the ones involved in CRPS thus making it more effective. It is also designed to not give the "high" (it is the medication given to help heroin addicts get off heroin) so it makes it technically less addictive.
My second wanted me on buprenorphine (the Butrans patch) because he felt it was better/safer for my body long term (do less damage) than Methadone. Again, it is a suboxone medication, so designed not to give the "high."
Norco and Percocet were completely ineffective for me.
The med that helped most with the burning was gabapentin (the base that Lyrica came from) in higher doses every day. I can't speak to a medication regimen, I'm not a doctor. But if your pain level is still high, there is certainly room to increase all of your med (I don't know about the Celebrex) quite a bit. (ok. in my opinion you are undermedicated).

The other thing would be a good PT program. Quality PT makes a huge difference. Desensitization, gentle stretching, etc.