What kind of dr should be seen for chronic ankle pain and swelling?

It depends. If you are young and the problem is related to physical activity, i would recommend perhaps your primary care physician or an orthopaedic surgeon. If you are over 65 and have heart or kidney conditions, you should visit your primary care physician. Hope this helps.
Ortho Foot and Ankle. Find an orthopaedic foot and ankle specialist. Try aofas.Org where they have a doc finder to help you.