It is clear that this is the other party's responsibility. What you need do is to (1) inform your own insurance company and contact the other party's insurance company (2) go to see doctors if you need, and (3) collect the receipts of your medical bills. Then you can negotiate with the other party's insurance company on the reimbursement. Don't accept their term too quickly.
Don't get a lawyer, because a large amount will go to the lawyer. Based on your description, your injury is not that severe, so it's hard to find a lawyer. And even if you can find one, after the law suit, you will have very little left.
Good luck. It will take some time and effort, but you should try it.
