While there may not be a particular law prohibiting filming yourself while driving, all states have laws prohibiting careless driving. Holding a phone to film yourself likely falls under the auspices of operating a motor vehicle in a careless or distracted manner.
However, it may be possible to mount a stationary recording device to film yourself while driving without diverting your attention from the driving tasks at hand. Refer to state-specific laws for careless driving in your area to ensure the legality of what you plan to do.