...actually some places do let you ride along with paramedics. some colleges and hospitals have programs where students can ride along. i don't really know the details, but i do know it's not a complete impossibility. i think if you talk to different places, and let them know you are seriously interested in EMS you might find a ride along.
Usually it's a liability issue, when I was in school for EMS and after, they only let people enrolled in an Allied Health program, or other medical program, ride along. Because they were covered by the school's insurance.
You might try volunteering at a hospital, and getting placed at or near the ER. Heck, the EMTs might even let you help hose out the ambulance...
My tolerance for seeing pain in others is not very high.
“I made you take time to look at what I saw and when you took time to really notice my flower, you hung all your associations with flowers on my flower and you write about my flower as if I think and see what you think and see—and I don't.”
― Georgia O'Keeffe