Similar but different to your situation, I've e-mailed/called several post-bac programs to follow up on my application this cycle, and as long as you're polite about it they usually don't mind. Just say you're calling to check on the status of your application/inquire to see if any materials are outstanding/wanted to know a timeline for when you should expect to hear back.
They deal with dozens (if not hundreds) of these kinds of calls daily, so be nice and sympathetic to their stress and make your desire known without pushing them. There probably is a limit to "too much", but once I called/e-mailed two different programs 3-4 times each in one week; one rejected me, and one accepted me so I don't think following up had too much of an impact (I was equally polite to both). Chances are if you get rejected, it'll be for other, bigger reasons (GPA, MCAT, LORs, etc.).
As for increasing chances, you can Google writing a "Letter of Intent" but be forewarned that is not something you should back out of, and will likely only push you over if you're on the fence. But maybe that's the extra nudge your application needs.
P.S. For those schools you've been rejected from, see if you can schedule a "feedback appointment" to see what parts of your application need strengthening - some schools will be gracious enough to grant you one, others will just say they have insufficient resources to grant such a request, but if you can get honest feedback from an admissions perspective on your application, I'd say why not!
