I didn't have shortness of breath, but felt that my ribcage was restricted, like a weight or something. I had a hard time getting deep breaths, and often if I laid on my back or side I'd have a panic attack, when standing wasn't a problem. Turns out that it was restricted. The ribs were stuck and didn't move normally when I breathed in and out. My husband is an Osteopathic Physician and spent a year just doing manipulation (of joints and muscles - similar to a chiropractor, but not as severe!!!) and is very good. He was able to get the ribcage to release and it made a HUGE difference. I'm sure it got that way with the pregnancy putting lots of pressure on my ribcage. My baby is nearly a year old and still if I get rib restriction again it can trigger my heart racing and feeling a bit panicky (even though my PPD has passed), so I try to get it treated quickly.
I'd recommend finding an Osteopathic Physician who practices Osteopathic Manipulative Treatment - OMT (many don't because they have no interest or were not taught much about it in medical school) and get checked out. If you can't find anyone in your area, then check with a chiropractor, but I don't recommend them first because they're really into high velocity treatments, lots of machines to diagnose and treat (things like small hammer pounding your vertebrae back into place...) instead of their hands, and sometimes some of them hurt people. So if you need to use one, do a lot of checking around to find a good one, they do exist.
I know this is no fun, and I hope you can get it resolved. PPD is no picnic, and neither is anxiety. Best wishes!