Hey, I struggled a lot with shin splints in high school too. It sounds a bit unbelievable but the thing that fixed it for me (almost instantly) was doing some of my running barefoot. Like someone earlier said, there's a good chance your form is causing you shin splints (it was for me), probably due to overstriding. If you're landing on your heels way out in front of your body, you're overstriding. Going barefoot automatically forces your body to run with a more natural form, and it strengthens muscles in your feet and legs that don't normally get worked because your shoes do the work for them. That could also be the cause of the other injuries you mentioned, but I can't speak on it personally. Since what you've been doing isn't working, I super strongly recommend it. You should be careful though, you're gonna essentially be changing how you run, and while it'll fix your shin splints, it can give you other injuries, especially when you're just starting. My recommendations that I mostly had to learn the hard way:
To start, just so you can see if I'm right or not, start your run like you normally do, ideally on a track or soft surface. Once you start to get shin pain, take your shoes off and just jog for .25 or .5 miles. I feel literally instant relief from shin splints as soon as I take off my shoes, but it may take a minute or two as your body adjusts. I didn't even need to try to change my form, I just stayed relaxed and my body naturally adjusted immediately. For your first time, .5 miles and a couple strides would be the most I'd do. If it helps, you can start integrating more of it into your training.
The most barefoot running I ever did was about 30% of 35mpw. I still did most of my running with shoes, but every week I'd do a 5 mile easy run barefoot, and 2-3 times a week after easy runs I'd do 4x200 on the track barefoot. If I was gonna do 5 miles with shoes but my shins started hurting, I'd normally just run 3 miles and then do 1 mile barefoot on the sidewalk as a cooldown. There were also some out-and-back routes where I knew I could take off my shoes for a mile then put them on otw back. My best track season (and the only one where I wasn't injured before the end) was the one that I ran most of the workouts barefoot. If we were doing 16x200 I'd do the first 4 with shoes, then go barefoot for the rest. If it was 4x1200 I'd do the first rep shod then go barefoot for the last 3. You shouldn't jump straight into that, but if running barefoot helps, starting to do some reps of your workouts barefoot is a good idea.
Just a warning: The first few times you do a workout or a distance run barefoot, your calves may be absolutely wrecked for a day or two. You can also get pretty gnarly blisters if you don't have callouses built up, but you build callouses quickly, and blisters aren't nearly as bad as shin splints. Hope it helps :)