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First thing - don't run through the pain and don't ignore it thinking it'll go away on its own. A lot of runners mess themselves up that way. If your shin hurts, you need to cut back on training for a couple weeks or switch to something else entirely - cycling, swimming, whatever, just not running.
Usually this kind of pain shows up from overworking your muscles or from bad technique. Check whether you've started ramping up your distance or pace too fast. If you're running in old sneakers with crappy cushioning, that's probably it - get yourself proper running shoes, they really do help. Try warming up your shin before you run, do some stretching after, maybe strengthen your leg muscles with basic exercises at home.
If the pain doesn't go away after a week or two even with rest - then go see a doctor. It could just be muscle fatigue, but it could also be a stress fracture or inflammation. You shouldn't mess around with that, better to get checked out by a specialist once than spend half a year limping around.
Shin pain is often caused by muscles and ligaments simply not being ready for the load you're putting on them. If you switched to regular running abruptly or bumped up your distance all at once, well, there's your answer. At first, it's actually better to dial back the intensity - don't stop completely, just shift to a slower pace or alternate between running and walking.
Pay attention to your technique and shoes. Sometimes the pain happens because you're landing too much on your toes or, the other way around, on your heels, instead of naturally spreading your weight across your foot. Running shoes matter too - a worn-out sole or a shoe model that doesn't match your foot type can cause constant micro-injuries. Try less intense running days for at least two weeks and see how it goes.
If the pain doesn't ease up after a week or two, keeps getting worse, or your shin swells up, don't put it off - it could be shin splints or something with your blood vessels. Warm up your muscles before running, stretch after, and don't ignore what your body's telling you. I came back to exercise after a long break myself - the mistake is jumping right back into your old pace.
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