Anesthesiologist will have more idea as well information in terms of giving anesthesia but he may not have idea on how to deal with pain in different condition. He can be useful only for pre operative anesthesia or local anesthesia. Where as pain management docotor will also deal with route cause of pain so it may not come back and patient gets cured faster as well for permanent for possible treatable conditions. Now to answer your question for reflex sympathetic dystrophy I suggest you consult first neuro physician and based on his advise and medication take a view of physiotherapist as well pain management doctor for further improvement. As per my view I believe the major issue with rsd is pain, swelling, and vasomotor dysfunction. And this can be treated well with regular exercise use of hot and cold pack for swelling and reduce inflammation too. As well with regular exercise work out body releases certain hormones to regulate the imbalance within the body and helps to heal the inner body. So also concentrate on curing the cause rather then just managing the symptoms of pain. One last suggestion as a physio and nutrition specialist keep more of omega 3 in your diet. It has anti inflammatory as well hormonal balancing natural property which will be helpful for you. Take care.