As with any disease, there are varying levels of pain experienced by patients. No pain at all would be unusual and may suggest a condition other than erythromelalgia. Pain is so integral to the diagnosis of erythromelalgia the word appears in most definitions (as seen below). To diagnose erythromelalgia without pain would have to be to the exclusion of all other possibilities. I would say it’s unlikely but not impossible.
Mereck Manual:
Erythromelalgia is a rare syndrome in which small arteries (arterioles) of the skin dilate periodically, causing a burning pain…
NORD (National Organization for Rare Disorders):
Erythromelalgia is a rare condition that primarily affects the feet and, less commonly, the hands (extremities). It is characterized by intense, burning pain of affected extremities…
Medscape:
Erythromelalgia is a rare disorder characterized by burning pain, warmth, and redness of the extremities.
Wikipedia:
Erythromelalgia, formerly known as Mitchell’s disease (after Silas Weir Mitchell), is a rare vascular peripheral pain disorder in which blood vessels…
NIH (National Institutes of Health) (US):
Erythromelalgia is a condition characterized by episodes of pain, redness, and swelling in various parts of the body, particularly the hands and feet.
NHS (National Health Service) (UK):
Erythromelalgia is a rare disorder that causes episodes of burning pain and redness in the hands and feet, and sometimes the arms, legs, ears…
Healthdirect (Australia):
Erythromelalgia is a rare skin condition which causes a burning pain, heat and red skin usually on the hands or feet.