What are the risks of removing blocked milk ducts and tightening of the skin around the top of the arms?
There are no milk ducts in the arm pit area. There are sweat glands called apocrine glands that in some patients cause excessive sweating or boils/abscesses. The latter is referred to as "Hidradenitis suppurativa (HS)" -http://en.wikipedia.org/wiki/Hidradenitis_suppurativa
May I suggest you check out this reference and see if it is of assistance.
Gary R Culbertson, Md, FACS