My mother has experienced this. In her case, it appears it was at least partially caused by her Sinemet dose being too high. (It was, I guess, considered to be some sort of dyskinesia.) She has scaled it back from 700mg daily to 550mg daily, and feels some relief. Also, the benzo class of anti-anxiety med, particularly Klonopin, provided some relief to her when this symptom was at its worst. But I am not sure that Klonopin is commonly prescribed for this shortness of breath from PD -- this may have been an off-label use. (Also, the benzos interfere with various drugs -- be careful.)

But tight chest muscles may also be part of the PD itself, at least for some people. Even though my mom's shortness of breath is probably 50% improved by reducing the Sinemet, it is still there to a lesser extent as she is waiting for her meds to kick in. This makes everything very hard to figure out.

I think that reducing Sinemet, increasing it, or adding another drug (like Amantadine or a "benzo" drug may be helpful), but of course I don't know for sure...it has definitely been trial and error for us! Best of luck to you -- it is a really awful symptom and I hope you can figure it out soon.