No. You have a workers’ compensation claim and a workers compensation claim only. The law says this:
§ 71-3-9. Exclusiveness of liability
The liability of an employer to pay compensation shall be exclusive and in place of all other liability of such employer to the employee, his legal representative, husband or wife, parents, dependents, next-of-kin, and anyone otherwise entitled to recover damages at common law or otherwise from such employer on account of such injury or death, except that if an employer fails to secure payment of compensation as required by this chapter, an injured employee, or his legal representative in case death results from the injury, may elect to claim compensation under this chapter, or to maintain an action at law for damages on account of such injury or death. In such action the defendant may not plead as a defense that the injury was caused by the negligence of a fellow servant, nor that the employee assumed the risk of his employment, nor that the injury was due to the contributory negligence of the employee.
“Exclusive†liability is a fancy way of saying the only thing an employer has to provide for workplace injury is workers compensation coverage. That means, medical treatment, compensation for time of work, and compensation for lost wages in the future or loss of use of a body part. Pain and suffering cannot be recovered.  If the employer is supposed to have insurance coverage and fails to do so, it changes the game. It opens up the possibility of making a fault claim (although most general liability policies exclude employees). If you find yourself in a situation which way to go and whether fault may be an issue, contact an attorney with workers’ compensation experience and get free advice.
Rogen K. Chhabra