Imagine some disclaimer about me not being a medical professional is written here.
This is all general advice for ankle injuries based off of way too much experience with them (note: there is also a lot of information out there about rehabbing injured ankles)
Back in the 1970's Dr. Gabe Mirkin coined the RICE (Rest, Ice, Compression, Elevation) for sports injuries, such as strains and sprains.
Since then, Dr. Mirkin has changed his mind on this, unfortunately, most medical doctors didn't get the memo.
(from this article)
Since applying ice to an injury has been shown to reduce pain, it is acceptable to cool an injured part for short periods soon after the injury occurs. You could apply the ice for up to 10 minutes, remove it for 20 minutes, and repeat the 10 minute application once or twice. There is no reason to apply ice more than six hours after you have injured yourself.
(cherry picking from this article)
Citing current evidence, Dr. Mirkin writes that it now "appears that both ice and complete rest may delay healing, instead of helping."
(As an aside, a nurse friend of mine told me that there's now some disagreement about taking NSAID's, such as ibuprofen, for this type of injury, but I haven't looked into it)
One of the best things I've found you can do for an injured ankle is to move it. A lot.
As soon as you can do so without pain, start doing ankle circles or spelling the alphabet with your foot. This helps to strengthen the ankle and keep it mobile (one of the main issues with resting an injury like this is the loss in mobility as it heals).
Again, if you can without pain, start spending more time on one leg. Making a cup of tea? Stand on one leg. Waiting for a train? Stand on one leg (note: you don't have to stand like this, just raising a foot off the ground an inch or so will do, people won't even notice). One of my favourite ways of doing this is to stand on one leg while brushing my teeth.
The real game changer for this is to do it with your eyes closed. Try and build up to brushing your teeth standing on one leg with your eyes closed using your opposite hand.
I've also found great benefit in working on the foot itself by working on arch contractions (note: yes, I'm aware it's not actually the arch of the foot that's contracting here, but that's what it looks like) and towel / paper crunches. Along with this, it's a good idea to work on the fascia on the bottom of the foot and give the calf muscles some love.
One interesting side effect I've found of strengthening the foot and ankle is that the arch in my foot became more pronounced, meaning my shoe size actually decreased quite a lot (in UK sizes, I went from 11.5 to 10-10.5).
Something else that has helped me a lot is ankle traction and voodoo floss (note: my injury was a dislocation with the ankle healing slightly out of joint. After seeing an osteopath to have it put back in, this helped a lot, but the above bits will do just fine if you don't want to do this).
One thing to remember with all of this, work both sides, not just the injured one. You spend a lot of time on your feet, having strong feet and ankles is always a good thing.