What should my next step be to recovery of sprained ankle?

About a week & a half ago I sprained my ankle during a hike. I had x-rays done & was told I only had a mild/moderate sprain, no fracture. I've been following the RICE method from day 1 & even started walking with & without my crutches while wearing my aircast. My ankle is slightly swollen & red, but overall the swelling has gone down dramatically. I asked my doctor what my next step should be, such as ankle exercises or stretches, but she said I should just continue walking. Should I be starting stretches, since my ankle seems to be feeling a little stiff? When is it okay to remove the aircast & start walking without it? Could I wear an ACE bandage with shoes to help strengthen & get around? Thank you in advance!