Short answer: yes--you can sue your ex-girlfriend. In Ohio, where I practice, I'm unaware of any prohibition against suing her. But more importantly, you need to consult with an experienced attorney who deals with insurance coverage issues to read your policy and determine whether there is indeed no coverage with your own company. The teaching lesson here is this: Many times insurance companies are WRONG in their conclusion that you have no coverage. I can't tell you how many times an insurance company took a wrong legal position over a coverage dispute. Do this: contact your company and ask them to put in writing where exactly under the policy it says you have no coverage. And then find a competent attorney to review their denial and determine whether their coverage denial was correct.
Remember, your company might be right about this. But they might be dead wrong too. The point is that you should NEVE R assume their position is correct just because they say so.