I run in these compression sleeves, which I think have done wonders for my shin splints.
I also use this arm band for my phone. It's very secure, but the actual band was too long so I had to fold it over and stitch it to make it shorter. I have skinny arms though.
I also have these bluetooth headphones because I'm a clumsy runner and kept yanking wired headphones out of my own ears. I've had them about 6 months and they work great. Two criticisms: they're a bit heavy, but really no big deal, and you have to maintain pretty much line-of-sight with your phone or they cut out (a pocket is fine, a wall is not). Not an issue while running obviously, but I often wander off when I'm listening to something at home.
I used to get insane shin splints when I first started running.
Stretch before and after a run of course.
Throw out your cheap Walmart shoes. Make an investment in some good shoes. They do not need to be insanely priced, they just have to over some good support.
The biggest thing that helped me was compression sleeves. They cost me about $40 but I've had the same pair for 3 years. They are amazing and now I don't even have to use them more.