Were there medieval hospitals?
Yes. The Hotel-Dieu of Paris is a very famous example. It was founded in 652AD by St. Landry, the Bishop of Paris. In the UK, Bath and York (St. Peter, later St. Leonard) are notable sites of famous hospitals. Hospitals were usually attached to some form of religious house, either a monastery or a convent, and often took their names from a patron saint relating to medicine or healing.