Hey fatty - running puts a lot of stress your muscles, joints, tendons and ligaments, particularly if you increase your training too much too soon. The general rule of thumb is no more than 10% per week then every 5 or 6 weeks drop back a bit and then pick it up again. If you keep your mileage relatively low to start and give your body time to adapt to running consistently 3-4 months, you should be able to run injury free as you start to step it up. I tried stepping up from half marathon training to marathon training distances too soon and seven months later I'm still dealing with consequences of a damaged achillies tendon and am only running 3-6km sessions.
I tore three ligaments in my right ankle doing taekwondo a few years ago - spent about a month in plaster and another couple of weeks on crutches and then a long time after that recovering because I started training again too soon - so listen to your doc and take the time now needed to heal properly or run the risk of being unable to run/exercise properly for 6+ months like me
To strengthen your ankles, try standing on one leg on a cushion or pillow. If that's too easy, add another. It's amazing how good a work out it is, even for your butt! Another one is to stand on a step and drop your heel - really good stretch.
Best of luck with your recovery