I recommend deep breathing exercises on a regular basis to expand your lung capacity, meditation to help you maintain a more relaxed state, and, if your doctor approves, some aerobic activity to strengthen your muscles to make breathing easier. When I began to work up to a greater aerobic capacity, I noticed less trouble with phlegm, which I've had a bit of an excess of for many years, and which had caused me to need an inhaler for a while after being very sick in my late 20s. I was surprised at this unexpected result, and it's one of the things that's kept me interested in pushing myself since.
My girlfriend has asthma and small lungs, and she jogs in the mornings. She built up the same way I did. Neither of us is fast. That's not the point. We simply began with walking, then did little intervals of jogging periodically along the way (between two driveways or telephone poles), then began to stitch together our little jogs. From my own experience, I told her when she began running in the beginning of the year one year, that she'd be running with me by the time the year was out. She had her doubts. But she got a nice surprise when she accomplished it by that autumn.
If possible, checking with your doctor is smart. I'm not a medical expert. But go with it once you get the go ahead. It may help a lot more than you think. Oh, and I don't know how old you are, but I'm 43, and my girlfriend is 53. We've only been jogging for the last few years. So, however old you are, don't let your age stop you. We're not the oldest to ever start doing it.
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