Is there a citation network crawler [tool] for building a bibliography?
This can certainly get tedious, and searching in both directions (i.e., using the "cited by" entries) is certainly the way to go.  That said, if you start at your university library, especially a medical library, you will have access to tools that are tailor-made to do medical searches, like Medline.

If you're having issues, by all means, go talk to a librarian.  Their job is to help people like you get their jobs done.  They absolutely love to do it, and they're usually very good at it.

To put things in perspective, though, 15 years ago the only way to do what you're trying to do is to wade through hard copies of the Scientific Citation Index and photocopy the articles after finding them in the Medical library stacks. (i.e., -- we used to walk thirty miles to and from work, uphill both ways!)