My Susie is a very rapid, hard mouth breather too. I also worry that she doesn't get enough air. I watch her carefully and have noticed that since she is so small and pettite, her litttle nose is very tiny too and she has a particularly scrunched up face. About the only time she isn't panting is when she is asleep. I have had her checked and there are no heart problems or lung problems at all. It is merely a fact of the breed that short snouted dogs have more trouble breathing (see Am. Bulldogs, pugs, etc.)...
Susie also snorts and sneezes a lot. I do know that she has some grass allergies, and this can also contribute to breathing difficulties. You might want to check for allergies as well. They can clog up sinuses as well as they do in people. Ask your vet about allergies contributing to breathing difficulties.
Otherwise, I've learned not to worry about it. Maggie also snorts a lot, even tho she has a longer snout than susie and a bigger nose. I just learned to live with doggie snot all over me and my apartment. :D
