If it makes you feel more comfortable (and it certainly would me) to have a second opinion, go for it. I would encourage you to seek a movement disorder specialist (MDS) - a neurologist who specializes in movement disorders such as Parkinson's disease.
As mentioned, there is no definitive test for Parkinson's - it's basically a process of elimination and then becomes a clinical diagnosis (meaning by observation - ex., arm doesn't swing as normal, gait not normal, etc).
I actually saw a neuro and 2 MDS. First two weren't sure - said could be Essential Tremor or PD - 3rd one was right-on. She has been my neuro/MDS since.
Best of luck to you!