Its not so much about your ability or intellect, its about your determination. If you truly want to be a doctor and are willing to work for it, it will happen. Although working as an EMT and/or paramedic does give you exposure, your desire to learn on the job is crucial. I'm an EMT looking to go to Physician Assistant school next year, so when I'm working either fire cars or IFT cars, I always try to learn something new. IFT wise, I try to do assessments, even if it is not necessary, I try to read discharge notes, drug admin sheets, etc. Also, building patient rapport is something that is difficult for many med students, so I encourage you to develop your patient interaction skills. When working with medics or as a medic, try to take note of what they are administering, why, and then later do some research on how these drugs work. Keep striving to learn on a daily basis, and I think you will get a lot more out of your job that will prepare you for a future in medicine.
As far as the prerequisites are concerned, you do need to take general chemistry, organic chemistry, biochemistry, general biology, physics, and calculus, as well as some psychology/sociology courses. Once you have finished the prerequisites, you will have to take the MCAT. Majority of schools look at your GPA and MCAT as a filter, then they look at your volunteer work, shadowing experience, work history, and any other community service you may have done. I suggest getting involved with a local hospital for volunteer work, many only require a 4 hour commitment per week, which should be easy to do. Anyway, sorry for the long post, but if you have any questions, please feel free to message me.