You can file a claim with your insurance company, but you may have to pay your deductible up front. Then your company will reimburse your deductible after they have completed subrogation with other driver's insurance company. The alternative to this would be to file a claim with the other driver's insurance company if the other driver is admitting fault in the accident. In that scenario, your current insurance carrier likely won't ever be notified of the incident, but your future rates can still be impacted by a not at fault accident since it will be listed on your CLUE Report.
Ultimately the choice is up to you but the severity of any impact to your rate is minimal compared to the impact of an at fault accident so I wouldn't let that discourage you from getting your vehicle repaired. I would also recommend checking out our tips on what to do after an accident