You would have to check with the insurance company that insures the company you are working for to see if you if you would be covered.
Usually if you are an independent contractor and not an employee, you are not covered under your employers insurance but I would check with them. They may be able to add you as an additionally insured.
If you are receiving payment for the massage, your student insurance wouldn't cover you. If you are not receiving payment, a student insurance policy might, but the clients would have to sign something saying they realize you are a student and not a professional, and this was part of your training.