Thank you for the reassurance everyone! I checked with the vet, and Beau does get his vaccinations against heartworm along with all his other vaccinations. He's currently up to date on all of those. So... sounds like it's not heartworm, thank goodness!
Bendy- I think Beau is just a loud/fast/panty breather too, so it's good to hear that it's not unusual for others as well. My fiance tells me that it's common in all labs and retrievers, as they are so active and excitable.
Golden- thank you for the reassurance, it made me feel much better! I will check with the vet about Bufferin. The baby aspirin is quite mild, I think, so Bufferin might make him a bit more comfortable when he's sore.
Overall, I'm thinking that Beau's breathing is just a combination of his soreness from arthritis and his usual weird breathing habits! Since he was vet checked and the vet says he is in very good health, I guess I just have to stop worrying and start listening to reason. It's tough not being able to see him every day, so I think that's why I am so anxious over his health. You know how it is with our babies!
Thank you again for the replies and welcome, everyone. I will keep an eye on him for now. And good health to all of you and your pups!