This is the Florida Medicaid website. Website is: https://www.flmedicaidmanagedcare.com/
Reading more about it, I'm not sure if you'd be eligible. Florida didn't expand medicaid under the ACA, so their requirements are quite strict. In states that expanded Medicaid, being below 133% FPL is enough, but in Florida it looks like you need to be disabled, pregnant or elderly as well. But if you qualify it should be cheaper for you than buying a plan on the exchange.
The other option is the ACA exchange. Florida doesn't have their own. Instead they use Healthcare.gov The sign-up period is from Nov 1st to Dec 15th mostly. But if you are very low income you can sign up anytime. People sometimes switch back and forth between Medicaid and a low cost plan on the exchanges based on their circumstances at the moment.
The only insurance options (other than you paying out of pocket for care)I can think of in the US are employer provided, ACA exchanges, Medicaid, Medicare for elderly, or Tricare for military.