Jason is right about VO2 max, and that if your body doesn't get enough oxygen your muscles will not be as effective. Getting a stitch while you run or progressively do exercise is quite normal, especially if you are just starting to exercise again. I don't know if you've ever done any exercises where you feel the "burn" or your muscles feel like they are swelling up, but this is what is happening in your diaphram. Your diaphram is a muscle that allows you to breath, as your rate of breathing increases this muscle works more. Then the pain comes in your side, and often times this is lactic acid building up in that muscle, which happens because it needs more oxygen. As you exercise more your muscles will become better trained, and so will your lungs. Your body will adapt to the increase in activity and need for oxygen. I do recommend asking a physician if you are seriously worried, but otherwise keep up the good work!
If it truly is a stitch, then what you are experiencing is hypoxia. That's just a fancy way of saying that you are not getting enough oxygen. I don't know what other activities you do, but performing some exercise that increases your VO2 Max would be helpful. VO2 Max is "maximal oxygen uptake". It is the most oxygen that you can take in at one time. If your body doesn't get enough oxygen, then it can't circulate throughout your body and that means your muscles will not be effective enough for what they need to do. It still might be a good idea to consult a physician, of course. Thanks.
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