Ah! Another sprained ankle!
I sprained mine 3 weeks ago now. Its still swollen but its not anywhere near as painful. It was/is a grade 2 and I still cannot do any high impact exercise as it kills if I try!
I don't trust my doctor so did a bit of personal research into grade 2 but not into grade 3, I hope it can be of some use to you but definetly stick to what your medic or phisio has said.
I found a range of exercises which would help the injury recovery rate. I found that as the ankle ligaments heal, they first develop a scar tissue. This scar tissue is brittle and if left alone can become hardened and pull on the calf and shin muscles. This in turn can cause a secondary injury so it is important to attempt exercises when you are ready.
For a grade 2 I went at it straight away- well I waited 24 hours. It hurt alot but I was too worried about the calf injury. I went into a swimming pool/jacuzzi and did exercises there. Exercises I did were things like spelling out the letters of the alphabet with my foot, or a figure of 8. Stopping to have a break when it got too bad. Its OK to start with the letters as large as you need then to make them smaller as you get a better grip on it and the immediate pain subsides. You may need several breaks. I did. But the swimming pool/jacuzzi helped as it sort of slows down and supports the foot at the same time.
Exercises on the bosu ball and lying legs straight out on the floor infront of you are also things to try.
As far as cardio goes, this was a tricky one for me too. My exercises are predominantly cardio with like 10% being weights so I was really worried about my ankle. I did find a way around it though:
Bike! This is fine to do but be aware that when you get off, you may then really feel the pain- I did. Make sure you start off small and learn what your pain threshold is. Do intervals or say 2 mins sprint, 1 min normal. This will get your heart rate up.
Arm cycle, just make sure you keep your hips still by holding all the tension in your core. Again, speed intervals are good.
Rowing- felt fine for me. Slight issue with having to trap my foot in the foot holder but learnt to hold the tension in my thighs and not yank at my feet! Probably a better way around it anyway!
If and when you are ready, the elliptical machine is great. As you don't ever completely lift your feet of the pedals its not bad at all. Its just getting up to a speed that can hurt so what I did was intervals but with the levels. With a speed of 130 (advised by a fitness pro) I kept 2 mins at a high as I can maintain level, then after the 2 mins, half the level you are on, eg if your on level 16, half to level 8. Maintain the same speed (130) for 1 min then repeat the above.
Swimming sounds like a good idea, but the movement of the foot- splashing in the water can cause alot of agro so be wary of this.
The general idea is that if you have a normal ankle sprain, its the side to side movements which are affected. As most people over pronate this would include walking and running. But as far as moving forwards and backwards, as long as it is literally one direction (the foot does not swing at all in any other sideways direction) your safe. But the problem lies in the fact that its very easy to move sideways, even just a fraction and. This. Can. Hurt. Alot. Trying to keep to cardio where your feet are firmly inplanted to the steps and only move forwards and backwards is the way to go in maintaining a higher heart rate with a sprained ankle but make very sure you are able to take this on. A grade 3 sprain takes 6-8 weeks to become walkable on, you are at 4 weeks, its still early days.
With other machines: the stairmaster, walking on the treadmill and etc, you'll likely need to give it more time. I had a grade 2, I was told 2-3 weeks before I could run. Its been 3 weeks and I cannot run still yet after 1 week I was able to walk on a steep incline on the treadmill and use the stairmaster. I'd say 8 weeks 'till you should consider running again and play it by ear for everything else.
Make sure you keep the ankle support on whilst working out- even just walking around you are at risk of tripping and landing yourself 10 steps back to where you started. Keep the support on until you are at home and go to bed or decide to do any stregnthening exercises.
RICE is still a good idea I was told- icing for the first 48 hours and then at key points following things like exercise of a busy day on your feet. Its also worth taking a stronger NSAID pill. I took Ibuprofen and paracetamol but was given a stronger NSAID pill (to deal with inflammation) and it made such a difference. Worth asking for something though your unlikey to get it without a prescription.