I was advised by a personal trainer/gym instructor a while back that I could have shin splints. I did a bit of research at the time and remember a few things:
1. They take weeks if not months to heal. It can be as simple as you think they are gone, you hit the treadmill, and they are right back again and your having to re-rest and start again from scratch. Everyone is different, everyone will recover at different rates. Its a chance to get to know your body better but also to be very patient!
2. The idea of resting is way off what is realistic. Everyone needs to walk to some degree, even if its to the bathroom! So its a matter of doing things slowly and as little as often and also wearing shoes that help. Barefoot is not the best thing apparently.
3. Some forms of exercise are supposed to be OK, stuff like cycling and using the cross trainer. I have found otherwise- I can cycle on a gym bike for half an hour, stop to get off and its back again loud and proud!
4. Supported trainers are helpful if you have a pronation problem, get trainers properly fitted by a running specialist shop, get proper fitted footwear for other activities -don't go for the smaller shoes as they look cuter or the larger boots as they look buff (you didn't say if you were male of female!) and try to get shoes that are supported in some way for day to day tasks. Ballet pumps for example will not help you.
5. There are some exercises you can do to help gain stregnth against over pronations which can cause shin splints. I am not sure if they are available on youtube or elsewhere (its worth a look) but see if you can get a specialist to show you rather then watching a video as your moe likely to do it right and get a result rather then at best doing nothing at worse worsening the problem.
6. You can buy things to wear to help with shinsplints, like leg wraps which go around your calves. While they don't take the problem away they do reduce some of the pain while working out (or they do for me anyway!)
7.Always keep in contact with your doctor, if shin splints get worse they can become stress fractures.
Its frustrating, but then tbh I have not ever been properly diagnosed with shinsplints (I just answer to all the descriptions and symptoms) I could well have something else but this is what I have researched and found myself.