At the time eczema, like many skin diseases, was viewed as a form of leprosy. This means you could of found yourself in a lepers hospital or if you were a crusader you would have been moved into the Order of St. Lazarus.

For treatment you may have been bled in order to counter an overabundance of black bile. Baths and herbs might also have been used, as well as rubbing certain oils on your body. Your greatest hope would likely have been visiting relics and praying for healing.

http://his.library.nenu.edu.cn/upload/soft/haoli/114/372.pdf