What can I do if I was driving for Uber when I was rear-ended in a hit-and-run but both Uber and my insurance are denying the claim?

You most likely do not have any recourse. If you were registered with Uber and had your Uber app on, you were engaged at that time in ride sharing, even if you did not have a passenger at the time, and that means that unless you'd bought car insurance covering your during ride sharing, you would not be covered; and if Uber's insurance only kicks in when there is a passenger, you'd not be covered there. 
The above said, it is based on the assumption that the insurer and Uber have correctly stated the terms of their respective insurance policies. You don't need to take that as a given. Review your policy and see what coverage and exclusions it has, and particularly what is says about ride sharing, driving for hire, commercial use of your car, etc.--if the policy does not in fact exclude coverage in this situation (or at least you in good faith reasonably believe it doesn't), you could sue your insurer in court for breach of contract (an insurance policy is a contract) and try to prove they should cover you. Similarly, if you think that you should be covered under Uber's policy from what you understand of it, you could sue Uber and/or their insurer; they will then have the opportunity to show you are not covered. (Before doing this, ask to see the policy: if they will voluntarily show it to you, you may be able to determine if they are right or wrong and avoid the trouble/cost of a lawsuit, if it looks like you are not covered anyway--though if they won't show it to you, you'd have to sue them in order to even see the policy.)