Unfortunately, you're entering a business with a relatively saturated market. In many cities, there are more EMTs than jobs, and employers can afford to be picky and choose only candidates within their narrow characteristic ranges. Some easy disqualifies include...
Age (many companies like emts over 21 years)
Experience (yeah, I get it, you have to start somewhere)
Driving record/criminal history
Interview skills (perceived as motivation, reliability, resourcefulness, etc)
Pre employment metrics (written exams, practical exams, lift tests)
Resume quality (you may have been thrown out of the race without more than a quick glance at your application or resume. Think about how to write and format them so as to emphasize your strengths and sell yourself. Why does this company need to hire you? Now?
Think about these elements and see what you can do to hone your heuristics presented self to these companies.
One more note... its my experience that your best chance of being hired (in any industry, but especially in EMS) is to network... and tap into these people. Ask when the companies are hiring, what they look for in applicants, who to contact or any tips for interviews. Push friends in the business to introduce you or make connections when necessary. Your class instructor is also a good person to network with, so its worth getting in touch.
Good luck!