No you cannot go to jail for owing medical bills or even credit card debt.
A lot of people are unable to afford to pay all or any of their high medical bills and the worst thing that happens is the medical bills get sent to collection agencies that then try to collect the money you owe them.
And then all they can do is sue you in court for the money. But if you don't have the money to pay the debt collector then they still won't get there money.