Do want to be a doctor? Then don't be a paramedic. I can't see how it would help your application, and it takes away a seat for someone who wants to do that for a career. It's not the same as taking up a spot training to become an EMT-B, since they're much quicker to train and typically have very high turnover.
There's something wrong somewhere in your application that a slightly enhanced patient contact role won't solve. You say you have no shadowing, which strikes me as a major black mark. The clinical experience you did gain was mostly post-rejection. Are you confident in your letters of recommendation? I doubt it's your GPA or MCAT that's holding you back, unless you only applied to the best of the best schools.
If I was in your shoes, I would've looked into shadowing earlier, and made sure to apply as soon as AMCAS allows it. How many schools did you apply to, and what kind of schools were they?
As a side note, I work both as an EMT-B on a private ambulance service, as well as an ED Tech. In the ED, I get paid better than paramedics in the field do with equal amounts of experience. I get to do more things, and I've been able to learn a lot from the doctors and nurses. It's also good for a letter of recommendation, since the doctor you work with will know you better than the doctor you've shadowed 15 hours. It also gives you a more honest look at what you're getting yourself into for a prospective career.
