Hey, I'm a senior in high school and joined cross-country as a freshman and stuck with it for four years. Besides the incredible interaction and just plain fun I had, I also learned a thing or two about running.
Like AFK Protector said, if you're flat-footed, you probably shouldn't run, and elliptical machines are your best bet. But if you aren't it just sounds like your ankles are a little underdeveloped for running. Here are a couple tips and tricks I picked up along the way.
For starters, shoes are important. Besides getting cool looking shoes, you need to find a cross training or running shoes which are designed for what you’re doing. Basketball shoes are the worst out there to run in because they encompass the ankle, limiting their functionality and weakening them quite a bit.
Besides that though, you could start doing some ankle exercises. Sit on the ground and raise your right leg up off the ground. In a slow, deliberate motion, circle your foot around at the ankle 10 times to the right, stop, then 10 times to the left. Same with your other foot. Simple, right? Also, after your workout, find some stairs or something similar. Grab something for balance, and then put the ball of your foot (the front part) onto the stair, with most of your foot (arch and heel) hanging off. Go up and down 30 times on one leg, switch legs, and then do it 30 times again with both legs. This exercise is pretty hefty, (depending on your weight) and your legs will feel sore as hell the next day, but its worth it. This primarily strengthens calves, but it helps the ankles out quite a bit too.
For general running though, you need to get form down. So much energy is wasted with incorrect arm motion or landing flat-footed instead of on your toes that you can cut miles out of your workout. The very basics are generally to keep your elbows at a 90 degree angle, and move them parallel to each other, no crossing in front of your body. All the muscles in your body are connected to each other, so sloppy arm performance leads to sloppy leg performance.
The easiest way to get good leg performance is to do some drills before and after your workout. The best one I can think of are called walk-overs, in which you bring your heel up to your butt, pull your whole leg through, keeping your thigh parallel to the ground with your knee making a 90 degree angle while your shin is perpendicular to the ground, and your foot is up. Plant the leg and go with your other one. Also, keep your head straight and arms moving at your sides like I mentioned above, alternating your arm out with your leg down. This shouldn’t be done slowly, but at your own pace as you develop as a runner.
This all may be a little confusing, so if you can, find some tapes of sprinters and runners during the Olympics or whatever. Slow down the tape and watch their form. There is no wasted motion at all because their form is so perfect. Good form leads to good running.
Thats the long and the short of it, and keep up with running, especially when you don't feel like it (unless you're hurt, then take a few days off). As an afterthought, if you can find some friends to run with, all the better. It makes running 90% easier.