Is there a citation network crawler [tool] for building a bibliography? Is there a service/software where I can feed a bibliography, say in BibTex format, and I get all “Cited By” references as a response? In other words, is there an automated “Cited By” crawler?

Background: 

I'm currently hunting down case reports about a rare disease, because I need more cases for a dataset (yes, about medicine).

At the moment, I am filling up my Zotero Library by manually walking through Google Scholar's "Cited By" feature. The first day of doing so was expectedly productive. Within a few hours, the article count went up very fast. But right now, each "Cited By" page yields one or two new articles and I have about 114 articles to go. That, in itself is great, because it tells me that I might have visited most articles within the citation network. However, towards this end, I need double-check for duplicates all the time and it's very time consuming. I find myself scrolling through entries, or searching, checking whether I might already have added a paper, or not.

This is so tedious.

The very reason to continue simply is the occasional discovery of a new cluster of case reports that were not referenced by the previous one—and I really need a larger number of cases for the analysis.

I wonder whether I should stop here and look at — Mendeley — PubMed etc.

but I'm not sure whether this would cut time or assure the coverage of most of the citation networks.

Suggestions, very welcomed.
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!)