You do not have access to your personnel file unless the hospital/employer was a public employer. If it was, you can obtain those records via a public records request. Not so from a private employer. The records sent to and/or on file with the Board of Nursing can be obtained by you via a public records request. You will want to know what is being reported to the Board of Nursing as this can result in an investigation and/or action on your license depending on the reasons provided for termination.
Some states, such as Massachusetts where I practice, have a law that requires employers to produce a complete copy of a personnel file within a certain time after an employee's request. Unfortunately, it does not appear Florida is one of those states.
This information should not be construed to be formal legal advice nor the formation of a lawyer/client relationship.