I would definitely involve your insurance company and let them know about the situation. The other driver's insurance company should be paying for your damage up to the limit of that policy, but if it doesn't cover everything then your current company should be able to help cover the rest. This could be through your uninsured or underinsured coverage
or your collision coverage
. You may be required to pay your deductible, but there's a good possibility you will be reimbursed for it if they settle with the other company. In terms of wanting a rental, the at-fault insurance company should be covering your vehicle. You will need to contact them to request a temporary vehicle replacement while yours is being repaired.