Hannajane, I am so so sorry you've had to go through this. EMG is a CRPS patient's nightmare. The correct diagnostic tool, and the only one I've ever heard of is a Triple Phase Bone scan. It's done by taking Xrays before and after a radioactive dye is injected into your veins. Bones affected by CRPS absorb the isotope differently than "normal" bone. Thing is the test is only about 55% effective, meaning a negative or inconclusive result doesn't mean the person doesn't have CRPS, but generally a positive result does indicate CRPS.

Don't fear the flu shot, My CRPS is full body now but with the right side not as bad as the left. I set limits for touching, making sure any Drs., Nurses, or Techs know that a bad touch could mean a scream. I don't worry about not seeming macho by saying this, some "Macho" guys would be whimpering shivering lumps if they had to endure my pain level on a "good" day.
Has your primary care talked of a referral to a Pain Clinic yet? Treatment speed can be key to contain and get a possible remission.
Also if your Dr. hasn't put you on pain meds yet try Aleve or Extra Strength Tylenol they're not much but with CRPS pain feeds pain and can only make things worse.
If you have Allodynia (feel pain from light touches or even a breeze) keep that area uncovered as much as you can or wear soft fabrics that won't aggravate your pain.
The baths are lifesavers but in a pinch almost any warm water can help, at times I'll just let warm to hot water from the tap run over my hands and even take my wet hand and use it to bring the wetness and heat to my upper arm.
We do what we need to do to get by... best of luck and soft thoughts always..