I met my boyfriend of two years at work on night shift. I'd been single for a year and a half, ish, and had done some online dating, had friends set me up, etc. Work was supposed to be my prospect-free zone, so I was pretty bummed that I had to start looking cute there too, lol. For real, though, he is wonderful, and it's awesome to be with someone who understands what this job is like. I have met a lot of other great guys in my two and a half nursing jobs - doctors, other nurses, security officers, etc., so I would say there's a fair chance that you'll meet someone you click with through work. If not directly, maybe your nurse friends can set you up with people they know.
I don't know of any medical/human services dating sites, lol, but I met some nice people through Match. I was on for maybe two months and then got off to focus on my new job. It's a nice way to get yourself out there and remember what it's like to date, but I didn't just love it; I know others who have met their partners online pretty quickly, though.
My advice: focus on the new job, making friends there, and rediscovering who you are without the last boyfriend. It sounds like a fairly recent break-up with a long-term partner, so it's good to spend some time on just you. (I know that is easier said than done - after five years with the same guy, I know I had no idea what to do with myself!). But it's nice to figure out who you really are on your own, so when you meet new people you can recognize who you naturally fit with. Just my experience, for what it's worth.