Doesn't sound like PD to me. Your tremor sounds more like an 'action' or 'postural' tremor, which isn't characteristic of PD at all - rest tremor is the classic symptom of PD, which means you WOULD see tremor when resting your hand by your side or laying down.
Also other symptoms associated with PD you don't seem to have: shuffling walk, balance problems, stiffness etc.
It's good that you're seeing a Neurologist of course, but I doubt it's PD - could be something like Essential Tremor which is much more common (and I think less debilitating) than PD. Good luck.