Need advice about serious issues in a private boarding school (New York). We are new to the US and don’t know what to do

Do not assume that your son’s current school will write a bad recommendation. Based on OP’s comments in this thread, a mutual parting may be welcomed by all concerned.

Hard to see any medical negligence here. Did your son follow the instructions given by the podiatrist & by urgent care (often prescribed medicines are administered by campus nurse, but not always) ?