Word of advice, although running can give you such a rush of adrenaline and get those endorphins going it cal also wreck your shins, knees and possibly your feet. Listen to your body and if it says everything is ok then good. If your shins splint don't get better within a week stop running. Ok just my opinion as I wouldn't want to hear that you're limping around in pain!
FYI- The Elliptical offers a great workout without damaging any body parts.
Just a couple notes on shin splints.
Many years ago I had bad shin splints for a year or more. I was running pretty hard and didn't want to take a break from it. I got substantial alleviation by doing a couple things.
1) Stretching hamstrings and calf muscles thoroughly before running. The stretching seemed to give my lower legs more "bounce" and fluidity so that the shock from the footfall was absorbed by the muscles and tendons and not transmitted directly to the painful area. I learned this trick from other runners who solved shin split problems the same way, and I've passed it on to other runners who were helped by it.
The best stretch for this seems to be: I stand facing a wall with my toes three feet from the wall, then lean forward so that I'm leaning on the wall with my elbows. Bringing one foot forward and leaving one foot still in its original place, I support myself partially on the forward foot and roll back and forth on the back foot to stretch the tendons and muscles along the back of that leg thoroughly, up and down the entire length of the back of the leg. Switch feet and repeat.
I also supplement the above stretch by standing straight-legged and touching my hands to the ground; and also doing deep knee bends while leaning forward and supporting part of my weight with my hands on the floor (so I don't burn out my knees with that exercise).
The stretching is the single biggest thing that seems to provide some alleviation; but the following idea helps somewhat too:
2) In my own case, shin splints seemed to be aggravated when I had a jogging pace with a short gait and lots of bouncy, up-and-down vertical motion and a footfall on the forward part of my foot (midsection-to-ball of my foot). I have a big frame (260 pounds), and all that vertical bouncing tended to put a lot of stress on my lower leg and foot muscles over the course of a long run. So it seemed to help out when I shifted to a faster running pace with a longer, rolling, horizontal gait and a footfall on the back part of my foot (midsection-to-heel of my foot). The latter gait shifts my posture back a bit and takes the shock of the landing away from the muscles and tendons and the front of the leg and shifts it more directly into my heel and the stronger back side of the legs. The lower, more horizontal movement reduces the shock, then I just make sure to run on soft surfaces like dirt or a treadmill and use running shoes with lots of heel cushioning so I don't tear up my knees.
I'll just note that alleviation of the shin splints wasn't immediate, since I had a pretty bad case of it and I continued a heavy running schedule even as I started stretching more and changing my gait. But the difference was noticeable within a week or two, and after a couple months the shin splints disappeared for good.
If the shin splints are particularly stubborn, there's always the next step:
3) Switching up workout routines always helps to alleviate a standing injury or irritation. I used to just run all the time. But nowadays as I get older I switch off from one day to the next between running and stairs. Stairs are a great replacement for a run because they are just as much of a cardio workout (or more), and they strengthen the knees and provide some other complementary support toward running strength.
That's just my personal experience on the shin splints. I'm not an expert though. YMMV.
I have a workout regiment that I do five days of the week.
fifty sit-ups and fifty stomach crunches together.
One-hundred and fifty push-ups.
Sixty leg lifts on each leg.
And I also do a relatively random number of pull-ups and flexes on a bar(let's say about eight pull-ups and twenty flexes on average).