Progressive will have 2 claims open. They will have yours for your med pay, for any medical bills related to this accident and pay up to your limits. Med pay is primary, so health insurance DOES not pay, (until) you exhaust your limits, then health insurance takes over and pays balance per your health insurance contract.
They will have a 2nd claim for the other policyholder for your car damages and your injuries, since you was rear ended. When you are done treating, then the 2nd claim will settle your injuries for the medical bills (which will be reimbursed under your policy) and then what is left over is your "pain/suffering". Don't worry, everything should be handled, just like 2 different insurance companies, but they have to open 2, (1 for you on med pay) and the 2nd for car damages and injuries.
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