Parkinson-like side effects

I told my psychiatrist about my stiffness, muscle ridigity, tremors, twitching and cramping. He told me these are possibly side effects and not some neurological disorder like my neurologist says. He even mentioned the word Parkinsonism. I've been on sertraline for 4 years and he says it's possible that the effects become more pronounced over time, so he thinks I should get off it.

This seems rather uncommon to me? Has anyone else experienced this? Maybe most people quit as soon as they get these symptoms. Unfortunately I was taking a bunch of benzos when I started with sertraline, which probably masked the side effects for some time. I don't remember having this the first time I was on Zoloft though.