You know I have wondered about that as there are things you mention that do seem to encompass both. CRPS can be caused by trauma, a pain contributor or in some cases arise spontaneously. It makes sense to me that it would be possible to have both, as pain from TOS could set off a cascade of nerve issues.

The caveat here is that CRPS is a clinical diagnosis given after everything else has been ruled out and no other reason for the pain is found. It is a diagnosis of exclusion which is why adequate workup is so important. Nerve entrapment is a big mimicker of CRPS and I imagine that TOS could be too. The most important thing you can do is make sure there isn't a mechanical issue that needs to be addressed. CRPS outcomes can improve greatly when the cause is removed.

Some people with CRPS choose to have sympathetic blocks done to see if their pain is sympathetically mediated but there are risks and these are not as popular as they used to be. Neuroleptic pain meds like gabapentin and nortriptyline along with gentle PT are frontline treatments. Oral steroids are also helpful in early stages. That may be an option for you to address some of the inflammation as there is precedent for using them with nerve inflammation ie: optical neuritis, etc. I took two rounds of prednisone 10 mg 3xdaily for 2 weeks early on for CRPS symptoms and it did help scale things back.

I think you are on the right path and while it is certainly worth raising the issue with pain management or a neurologist you should still pursue possible causes for your symptoms and treat accordingly. In the meantime keep taking good care of your self and see if a med option (sometimes it take a few tries on this) will get you more comfortable so you can more easily move forward.