Something to remember about ulnar neuritis (and carpal tunnel as well) is that they don't show up on EMG for a few weeks after symptoms start. This is the opposite of A/L/S, which typically shows up on EMG before symptoms start. Ulnar neuritis can cause twitching, as can any neuropathy that affects motor neurons.
Having said that, I had similar symptoms. When my twitching started, I had a lot of ulnar nerve issues, to the extent that my neuro said I should wear a wrist brace and try to keep my arm straight during sleep. My ulnar nerve issues have gotten somewhat better over the past year, though the twitching remains (at a lower level, though).
You should make sure you don't have mechanical irritation of the ulnar nerve, which can cause weakness in your hand (it's like carpal tunnel, but on a different nerve). Ulnar neuritis is very treatable, so keep up with your neuro to make sure you're doing what you need to in order to keep your ulnar nerve happy.