The answer is that you can't be diagnosed with CRPS if the only clinical sign or symptom you have is pain, regardless of how bad the pain is.

The diagnostic criteria for CRPS require a number of signs and symptoms to be present across several categories. They don't all have to be there at the same time but they do need to be or have been present. It is possible to have chronic pain or chronic neuropathic pain following trauma and not have CRPS. All other possible conditions and causes have also got to be ruled out before CRPS can be diagnosed. The diagnostic criteria are not that complicated and you should be able to find them fairly easily on the web.