First of all I wish to say that I am NOT a doctor, but I worked with elderly, mentally infirm people for a number of years ... that's people suffering with various types of dementia (organic brain failure) ... and I can tell you that, based on my experience, you CAN develop Parkinsonism, which is NOT the same as Parkinson's Disease, from taking medications.
Whether you can actually claim compensation from the drug company/ies that make or sell the medication, I'm afraid I can't help you as I don't have any legal qualification(s) either.
If you believe that you may have a case, I'd suggest that you speak with a lawyer/attorney to find out where you stand.
Sadly, I'm of the opinion that you'd be unlikely to win compensation but, as I said, I don't have any legal training. A lawyer/attorney may well believe that you do have a case.
One argument that I could see a doctor throwing against you would be that, taking all things into consideration, it might have been deemed a necessary risk to aid you with your other problems. This does NOT mean that I think that's right. I most certainly don't.
Some things that will be taken into consideration would include how long you've been taking the medication(s) that you believe have caused your symptoms; whether you were made aware of any side-effects that could happen from taking these medications; your doctor's response to any complaint you made about how your symptoms were getting worse; whether your doctor actually made changes to your medication; and perhaps a whole host of other things.
Unfortunately, my friend, drug companies tend to be massive corporations that have enormous profits and doctors/researchers which they could plough [plow, if you're one of my American cousins] into fighting their case. This COULD mean that a court case could last for years and years ... even to the point that you'd have passed over to the 'other side' before any case is settled.
The biggest difficulty I envisage you coming up against is that it's doubtful that you could find a doctor willing to stand up against the drug company/ies and argue that it is DEFINITELY as a result of you taking these medications that caused you to develop Parkinsonism. Who's to say that you wouldn't have developed it anyway? This, in my humble opinion, would be one of the arguments that said drug company would put forward.
If you do decide to check out whether you have a case or not, I wish you the very best of luck.