Not sure about the heartworms, but my mom and dad's one cat had breathing issues when they found him (or he found them.. he showed up on their doorstep wounded). He didn't have heartworms, he had something called LungWorms. I have never heard of it before, and I don't know they there was much available back then to treat it, but I don't think he has it any longer.

Can the vet do anything to check and then treat for either of them.

Heartworm is pretty serious, so I don't think I'd just wait for them to go through their cycle. They treat dogs for it, so maybe the vet can do something for your kitty if she has it.