One thing that has helped me with breathing (and consequently singing) has been taking voice lessons with a real voice coach. I'm talking operatic lessons here - the real thing. The key with these isn't to learn how to sing in Italian. The key is that a professional voice coach will teach you how to relax your neck and vocal chords to allow you to sing without overdoing it, without cramping muscles, without pain. And by learning how to maximize the use of your diaphragm when breathing, you can make the most of the lung capacity you do have. The results are amazing; I learned not only that my true range is mid-tenor and not baritone, where I had been singing for years, but also that when I was in my true range and relaxed, my voice had ten times the power I had thought possible. So voice lessons with a professional coach will make an astounding difference.
The second thing I'll toss out - YMMV - is to analyze your diet and make changes. In the last four months my wife and I moved to a vegan diet, for different reasons. She is trying to address some chronic pain issues and I have to manage heart failure issues, which usually do not improve with time unless you focus on it. I've lost weight and all that, but also found that I have a lot less crud in my sinuses and trachea. I attribute this to moving away from dairy foods - milk, butter, cheese (much as I like them) which correlate with increased mucous production. I am also on the mend from a nasty lung thing that is going around town, and this time did it without needing antibiotics. Usually the concern is pneumonia, but this time my system seemed to handle it without help. I think getting away from dairy is helping.