What you have is a "stress reaction." It's the condition that occurs just before a "stress fracture." Consider yourself lucky. I had the same issue.
It sounds like you have posterior shin splints? Does it hurt on the inner side of your leg? I had these very bad about a year or two ago. Custom orthotics didn't do jack for me. I went to the doctor and told him what I was training for and he sent me these really stiff pieces of shit. What I really needed was something
flexible with an extremely high arch support. I tried superfeet, but it wasn't high enough. I found these things called Sole Ultras (
yoursole.com) at the New Balance store in Santa Monica. They're great.
You need to stop running on the track too. That's only going to make it worse. If I run the all-weather rubberized track too much, I get shin splints. It's too bouncy. Run the track only once or twice a week. The rest of the time you'd be much better off to run trails. Trail running is only going to strengthen your muscles and that's going to help prevent further injury.
Another problem I had when getting back into it was doing too much too quickly. I know what it feels like to want to get out there and run 5k, but you can't do that. Start out easy and slow. Too much too quickly will send you back to zero again.
I don't really have an opinion for your bike question. I bike a lot and feel it does little for my running. That said, most of the stress is put on your knees in biking. It's the impact on your feet that is your problem while running.
Last piece of advice I have is to not let your head get in the way. I battled this crap for a year and tried listening to other runners, doctors, physical trainers, etc. Eventually I was convinced that the doctors didn't know shit about my particular injury. It seemed like I was doomed forever. Don't let that get to you. Don't just accept what a doctor says as gospel. Get some books and do some research on the lower leg muscles and shin splints. I have no doubt that you can find the correct solution yourself if your doctor isn't helping. That's what I had to do, despite going to a fancy west-side doctor. That said, don't do anything stupid to make it worse! No skateboarding, no hip hop dancing, avoid jumping, and uh...I don't know...those are stupid random things I found to make it worse, haha.