Can I sue someone who hit my car even if insurance covers the damages?

Without additional facts it is difficult to say. 

You may sue for your unreimbursed damages regardless of your deductible. 

For concrete answers to this question it is probably best to call an attorney for a free consultation to discuss the specifics of your accident.

Chris Davis
Award-winning personal injury attorney and founder of Davis Law Group, P.S. in Seattle, Washington.