How long before my sprained ankle is healed?!

I sprained my ankle about 4/5 days ago slipping . I tore a ligament but I can still walk and encouraged to use it and my kind of sprain gets better with ankle excercises. I had an x ray no fractures. Theres bruising around the ankle kinda big it looks painful. My ankle hurts more in the evening. I can actually walk quite fast nearly my normal pace in runners/sneakers. I wore my runners in to school for the last couple of days as I can't wear school shoes. But one of the teachers told me I can't wear them and I'm to be in my school shoes. Or I have to get a doctors note which I haven't got time to get. The doctor advised me to wear anke support shoes. I've already been there there. I tried wearing shoes in today I could not walk as well as I can in runners made me walk a lot slower my ankles hurt the shoes were tight. I could've damaged it more. My ankle is still a little swollen. I'm a member of the gym how long before I can go back and use the treadmill or be able to run/jog. I heard swimming is good when is it god to go swimming can I got swimming if my ankle is bruised and its big and will be noticable. Do I need to wait for the swelling to go completely?What shoes is best to wear?
How long will it take for my ankle to heal?Whats the best ankle support shoes to wear?