Runners - I need your help!

Most people would tell you to, first, get some decent shoes.
I suppose you are not going very far. But you do have shin splints. So having a pair of better running shoes couldn't hurt and, if you are serious, you will one day be running the kind of miles where they are necessary.
When I first started running, I was a two-pack-a-day smoker. A former soccer player. But a serious smoker. I could not go more than once around my apartment building.
So, that's what I did. Once around the building, for a while. Gradually, organically, I began to go further and further.
I think my initial short distances and very gradual increase were key. It kept the thing fun -- or at least not so demanding that I came to dread getting out the door the next day.
KEEP IT COMFORTABLE!
If 10 minutes is all you can do, do that. If it causes shin splits, go less. Then don't push. Keep it at 10 minutes or less until the shin splints go away. You'll know when you are ready to go a bit further.
I see so many people who want to get fit or lose weight after being sedentary go out and kill themselves wanting to transform in a month or two. They start with the best of intentions, and then a month later they have stopped -- and essentially they have accomplished nothing. Fitness takes time. Those people who look like Greek gods did not start working out a month ago, or even six months ago. They have probably committed a life time.
So, you should acknowledge that. It ain't gonna happen over night. You've got to be in it for the long haul, and that means you have to like it. Or, learn to like it. The way it is fun and comfortable is to not push too hard. Not at first. The people who stop, often are working too hard -- pushing to run a 5k in one month, or spending an hour in the gym sweating and gasping! So, the next day they wake up, and the prospect of repeating that torture is looming ... and they really do not want to do it. So, eventually, they don't.
You don't want to be that person. Do less at first and you will do it for longer, which is the key. It will become a part of you, if you let it.
You will get to the point where you can work really hard in a session and like it and have a sense of accomplishment. But that will be when you get in good enough shape to do that. (Hint: Working out is not so painful when you are in shape ... But that takes TIME! Months, at least. Maybe years.)
As for shin splints, everyone gets them at some point in a running career. There is no specific treatment. You just back off on the running until they get better.
Try just running a block every day until the pain goes away.
Or take a week off if it hurts too much, and then start with a one or two-block run.
As I said, everyone (I know) gets them, and they get over them -- if they didn't, there wouldn't be so many runners.
Good luck!