Hi Norman, and welcome to technet. If you're looking for help creating a product, you might look into hiring a consultant from off of a site like elance.com, filemakerjobboard.com or a similar site for freelancers. People here on technet are looking to help other developers figure out their roadblocks, but not necessarily develop solutions for you.
That being said, it looks like what you will want to do is a prime candidate for a CWP (custom web publishing) solution. A runtime solution is hard to keep tabs on if you add tons of users, and it doesn't really allow great ability to centralize and control your data. From a custom web published solution, you could create a robust login system based on a table of patient numbers, and be able to recall/delete users' access remotely, and see who's been logging in in realtime.
I'd highly suggest investing in a consultant to help you out though, especially if you've just started building a product from the ground up. Medical solutions need rock solid development because downtime and waiting for bugfixing is usually unacceptable (from my experience).
A FileMaker runtime will not work with FileMaker Server. Mike gave you very sound advice. Creating a mission critical medical solution requires a very high level of FileMaker expertise.