This is a difficult question to answer, because the writing of the Medieval period is broad and difficult to work through. In other words, there is so much of it. However, there has been a number of works that deal with this topic to a certain degree. The basic point of these works is that hospitals were a Christian invention.
Based on this point, we can say that the church helped the progression of medicine, generally speaking. I am sure that many people can bring up counter examples. Notwithstanding these counter examples, the church has generally aided in the progression of science, technology, and medicine. This point is often times lost in polemics. A great book on this topic comes from a Harvard anthropologist, Stanley Tambiah. His book is called, Magic, Science, and Religion and the Scope of Rationality.