You're question lacks a little bit of detail about what your workouts looked like, but general causes for exercise related lower leg injuries are:
Running too fast, puts massive strain of the soft tissue around your shin bone. The only way to cope with this is slowly built up your exercise to allow the tissue to strengthen. Run at a speed that you're still able to speak is a nice rule of thumb for not running too fast.
Running on hard surfaces, if you're like me forces to run in the suburbs, your feet hit the pavement hard with each step. This causes the same problem as my previous point, it will just happen faster on hard undergrounds. If you can: go to the woods or a park.
Running with bad shoes, while the barefoot running crowd may disagree, running on old or plain wrong shoes is bad. Old shoes have degraded EVA, which has bad or inconsistent cushioning. Using your aerobics or tennis shoes for running is also a bad idea, because while they may look similar, they are really built completely different and often of different material as well. Getting a pair of good running shoes will go a long way of reducing your chances of injury.
If all else fails, you could get a pair of orthotics (don't overpay!) or compression stockings. The first helps reduce movement of your foot in the shoe or make slight corrections to your feet roll off pattern. The latter keeps your calf muscle in place and thereby reduces the stress on the soft tissue a lot.
The last part I can really recommend: get a training plan. I'm sure you've tried one before, but this time get a training plan and cut your goals by 20%. So instead of aiming to run at 10 km/h start out at 8 km/h, instead of trying to run for half an hour, start with 20 minutes. Also, I can really recommend a program like Start to Run or your C25K, this forces you to alternate between walking and jogging for at least the first few weeks. This greatly reduces the total stress on your soft tissue and should give your body time to start adapting.
But remember, even when things start to get better, stick to your plan!