Anxiety is a very common non-motor symptom of PD. It was one of my first non-motor symptoms 20 years ago, before I was officially diagnosed with PD 3 years ago. I treated my anxiety with an anti-depressant after many years of struggling with it and thinking I could over-come it on my own. I have taken Paxil for many years and although most people think of it as an anti-depressant - SSRI drugs such as Paxil are "a fix" for anxiety as my doctor explained to me - not just a temporary band-aid like Xanax would be (Xanax is also very addictive and not a good drug to take everyday unless prescribed by your doctor). Paxil was so effective at relieving my severe anxiety that I expect I will be on it for many, many more years.
If your doctor does prescribe an anti-depressant for you, start out with a super low dosage to avoid any uncomfortable side effects in the beginning. I started with a 10 mg tablet (not capsule) that I cut in half for a 5 mg dose and took that for the first week or so and then upped it to 10 mg for the next week and then very slowly upped it to the dose my physician prescribed for me. This way I avoided all side effects, which can be very disturbing for a week or so, if you start on a higher dose.
That was my experience. Hopefully it will be helpful for you.