sherreys is right -- getting the license is only the first hurdle. Most healthcare employers now do criminal background checks on applicants (many states require
this; mine is one), and it is entirely their right to refuse to hire you because of your criminal record, if they choose to do so.
Some employers will be willing to take a chance, some will not. It sounds like your conviction didn't involve any violence, predatory behavior, or drugs (not by you, that is), so you may be okay. There's no way to predict how you will fare, though.
Best of luck!