If you are hit by an uninsured motorist then you would normally put a claim through your collision coverage or if you do not have this type of coverage then through your coverages for uninsured motorist property damage (UMPD). Not all states offer this type of coverage however if you do have UMPD then you could make your claim for your damages this way. You may only have UM (Bodily Injury) coverage.

Now we cannot tell you for certain if your insurance policy, specifically your UMPD, pays for a rental car since we do cannot see your policy terms however rental cars are not normally covered by uninsured motorist coverages.

It depends on the state and policy, but typically UMPD (and/or UMBI) do NOT include a rental car allowance. You can read through the terms of your policy on your own however it would appear that you checked with your insurance agent to see exactly what uninsured motorist policy covers and the agent told you that a rental car is not part of this coverage.

UMPD or UMBI is not intended to a cover rental car. You would normally need to have RREIM (Rental Car Reimbursement) coverage to get a rental car paid for by your insurance company as part of a first party claim. RREIM would give you an allowance in which to rent a car while yours is being repaired.

If you were making a third party claim against the at-fault party, if they were insured, then normally their property damages liability would cover a rental car. You may want to see if in your state you can sue the at-fault party for the rental car charges and any other expenses related to your car's damages that your uninsured motorist coverages will not cover.