I wouldn't focus too much on the "stages" of CRPS...I think that is generally considered old thinking because people go through stages in different orders, are in one and then can go back to it later, skip stages, etc.

There are definitely some key things that SOUND like CRPS but many times CRPS is a diagnosis of exclusion (rule out a bunch of other stuff and then you know if it's CRPS) but it is good that they are identifying it so early. Even if it ends up not being CRPS it's far better to treat it like it is until you find out it's something else because there are certain things that can make the CRPS worse and cause it to progress further/be harder to get to remission.

So in the mean time while you wait to see pain management and neurology...avoid ice/cold as much as possible as well as immobilization. Immobilizing is bad so even just stretching exercises are good if weight bearing is too hard.

My CRPS is on it's 10th year and for me it has always been cold. The pain itself is burning but the temp change in my various CRPS areas is always it gets very cold and that started happening almost immediately. It was the first symptom aside from the intense pain that was an indicator of CRPS (and was ignored by every doctor until I got to a pain management doctor). But I also think that many things were done in the beginning (ice, immobilization, etc) that caused my condition to progress faster.

Unfortunately I never responded well to medications or other treatments. In December of 2017 I got a DRG Spinal Cord stimulator and that has been life changing for my CRPS pain in my left leg from the knee down...so I am mobile now at least. But heat always has helped so if you can, maybe try some warm baths with epsom salts to give you some relief. Because you are only 3 months in, you may respond better to some of the treatments like sympathetic blocks or medications and physical therapy. Many, many people go into remission if they catch it early enough and treat it properly.

I wish you all the best luck in sorting this out.