Well, let me offer you my story, and it may help you make a decision. I'll say first that I think you should go ahead and complete a bachelor's degree of some type now before diving off into the world of EMS.
In Jan. 2001, I took a night class and became an EMT. I did it because I like being prepared for things and thought it was more suitable for that purpose than first aid (and it is), and because "medical stuff" was (is) an interest of mind so I assumed that learning anything there amidst the clinical exposure would give me a leg up in the premed process.
Things involving math weren't my strong suit then. I made straight A's through about sixth grade when my math skills started to wane. They continued to plummet. That said, I graduated high school, having never taken a course in chemistry or physics because I didn't want to do the math. Everything else academically was easy, and for the most part still is. At any rate, I found myself taking chemistry courses in college, and they were the only classes I had on Mon, Wed, and Fri. Because I'd never had that exposure before it was challenging, and it was also boring to me because of both the math and the idea that I could've been out doing other things that I perceived as more pleasurable. After that I postponed my "premed-ness" until I was ready to either retake them and make A's or relearn it on my own and move on to organic chemistry as well as physics.
A year passed, I became affiliated with a Volunteer Fire Department which I maintained for six years until moving, and I started doing first responder-type activities, I got the EMT bug and sat through paramedic school at night while taking all of my typical college classes during the day. I was enrolled at two colleges without one knowing of the other, and I took 30-36 credits each sememster for three semesters. I got my B.S., and my paramedic certification in Dec. 2003 having graduated college early. However, I never did talk myself into focusing and taking o-chem and phys.
Six years have now passed, and I've learned a few things including the fact that yes it's easy to get burned out as a paramedic particularly if you throw that on top of an already stressful career (biology teacher), you regret not doing things more than you regret what you've done, and I can do whatever I decide to.
I eventually quit both teaching and paramedicine and became a cop which I like (but dont love), yet I really regret not having gone to those chemistry classes six years ago. I've regretted my path almost daily.
