Re: the swimming thing. Yes, swimmers do have higher body fat than other athletes. On the other hand, the difference is only about 5% in comparison with runners. Twelve versus seven percent. Big deal. And that’s if your focus is only on swimming or running. People who do other training in addition to or in rotation with swimming would have slightly lower body fat than dedicated swimmers. Most single-sport athletes don’t really care about anything that doesn’t have a direct impact on their performance, and so don’t spend any time on training outside their discipline.
Regular people, on the other hand, are (or should be) doing a variety of activities because specific adaptations optimizing your body for a particular activity present trade offs. Long distance runners can’t carry much muscle mass. Bodybuilders have relatively low endurance. Swimmers have slightly higher body fat and almost the same bone density as non-athletes. Cross training, non- sport-specific exercise avoids most of the specific adaptation pitfalls. In other words, do a variety of stuff, keep doing it, and try to do more of it.
People keep recommending running as a way to get in shape when it’s actually a intermediate to advanced form of exercise. Boggles the mind. If you’re already overweight, then you’ll have a higher chance of injury from running. If your muscles and connective tissues aren’t in halfway decent shape already, you’ll have a higher chance of injury from running. If you’re really determined to run, do some conditioning and lose some weight first, and take up running after you’ve done some preparation for it.
Do some low-impact aerobics or swimming along with some beginning weight-training exercises. Take it slow at first, listen to your body, and take at least a day off in between sessions for the first couple of weeks. Former couch-potatoes along with other inexperienced and unconditioned athletes hurt themselves quite a lot because they rush, because they read too much about the advanced training techniques of elite athletes and what works for those people.
If you haven’t been running, you probably don’t have shin splints; they’re usually a repetitive stress injury. Since you said you’ve never been able to run without hurting, you’ve probably got some kind of structural or postural problem. This might or might not be correctable with specific exercise. Strength imbalances are often a cause of pain or injury in running, and bad technique either contributes to or causes the imbalance. Besides seeing a physical therapist or sports therapist for an actual expert opinion, there are two things I can recommend.
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Check out Pose running. The exercises and drills they do to get you ready for running will probably help with most correctable body imbalances. The technique taught in Pose is also an efficient and biomechanically sound way of running. If you’re going to start from scratch, might as well start out right so you don’t have to retrain yourself later.
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Try a few sessions doing some easy, short-distance running with bare feet on a soft surface, like a grassy field. If running with bare feet doesn’t cause significantly less pain in your legs than running in shoes, I’d be very surprised. You probably will get a bit sore afterward in some odd small areas. I did the first few times I ran barefoot because it makes all those little stabilizing muscles and connections in your lower legs and feet work more. Besides strengthening stuff, barefoot running will also auto-correct some bad technique; you usually end up looking quite a lot like Pose after a few hundred meters.
Neither of these is a panacea, though. If you’ve lost weight, gotten some better tone, done a few weeks of strengthening exercises, stretches, and drills, done some short barefoot runs after all that, and you still hurt while running, then you probably should not run.
On the other hand, you don’t need to run. The best outcomes in changing body composition come with a combination of strength training (weightlifting, calisthenics) and aerobics. Anything that gets your heart rate up and keeps it at 60–80% of your max will do just fine for aerobics. Elliptical, stair climbing, rowing machine, stationary bike, jumping rope, or a combination of all of the above will work for that. I got a link that gives quite a lot of information about novice weight lifting from someone here on the boards in an earlier thread on getting in shape. It’s mostly cribbed from a book called Starting Strength.