How to treat severe contact dermatitis from allergic reaction to neoprene in ankle brace?

You might need. Systemic corticosteroids if it is a severe reaction. Otherwise it could be manged with high potency topical steroids. See your physician to determine what is best.
Contact Dermatitis. Try wrapping your ankle with gauze or something gentle to avoid your skin coming in contact directly with the neoprene. You could also try neoprene or latex free ankle braces. Avoiding direct contact is best.