What if I did not leave the scene of my Florida car accident in an ambulance? Can I go to the hospital on my own the next day?

Absolutely, in fact I highly suggest that you either go to the hospital or seek other medical attention for any injuries that you may think that you have received as a result of the accident. Just because you didn't feel the effects of the injuries right or immediately after the accident that doesn't mean that you weren't hurt. A lot of times you won't feel the effects of those injuries until a day, to or possibly several days later. I highly suggest that you do seek medical attention if you feel like you were injured. That may or may not be at a hospital, but just so you're aware there is no requirement that you have to be taken to the hospital by ambulance in order for you to recover any type of compensation for your medical bills.