CRPS is thought to be a heterogenous syndrome, not one disease. IOW, it can have different causes.

In my case, it would appear mine is linked autoimmune problems. I have some more common or at least more well defined autoimmune problems (like Addison's and thyroiditis) and some rarer ones. Like you, I have gastroparesis. I also have small fiber neuropathy, POTS, and Ehlers-Danlos syndrome (hypermobilty type). All of these last ones are linked to the CRPS. People with CRPS are more likely to have any of all of these than the normal population. So in this way, I don't consider CRPS a stand alone disease in my case. IVIg actually helps my CRPS, POTs and gastroparesis, adding more evidence that these diseases are linked and autoimmune in my case.

I, too, have migraines. I think they are considered more common with CRPS but they were diagnosed separately.

You should go to the doctor of course but if it's not obvious, mention the CRPS. The doctor may not know what CRPS is but some of my linked to CRPS diseases (any of which can occur individually) were diagnosed more quickly because the associations I mention.

In short, yes, I do get severe headaches.