Since he was just vet checked I wouldn't worry so much. My girls have always had arthritis and like us when were in pain we breathe heavier
I'm not sure about dogs taking Aspirin? I was always told by my vet to give Bufferin 500 mg and it's safe up to 2 or 3 times daily if needed best on full stomach of course. It helped mine tremendously maybe you can check it out with your vet?