I sprained my LCL a few months ago. I started swimming and that really helpd. Swimming increases blood flow to the area without any impact. Increased blood flow really speeds up the recovery process.

I've had serious. The end of my femur fell off. Osteochondritis Dissecans, basically the bone and cartilage lose blood supply. I spent 4.5 months on crutches and had some pretty major reconstructive surgery. I'm a competitive tennis player looking to play D1 college tennis, so this was a pretty big setback. Oh, and I also tore a ligament and some cartilage in my wrist. Not that I'm a mess or anything.

Anyway, I'd recommend swimming for sure. It's a great way to gain/maintain fitness and strength while keeping the stress on your injury to a minimum. And as Payam said, the increased blood flow can be very helpful. I went to the pool everyday for several months, and it definitely made a difference in my recovery. I would also avoid icing, as it might even slow healing.

Re: Nutrition, make sure you're not deficient in any nutrient. Plug your foods into cronometer and make sure you're hitting everything (except maybe vitamins e and d). Zinc can help, but you don't want too much to throw off the copper balance. Vitamin C is necessary for the formation of new tissues, as is glucose to make glycoproteins. I'd up your carbs to 150 or even more if you haven't already. Potassium is very important for all cells, and sodium ions help it get into cells. Make sure Vitamin D is up to 40+. What does your diet look now? And you mentioned supplements, which ones are you taking?

Paul Jaminet has a post on injuries and nutrients here: http://perfecthealthdiet.com/?p=705 (from my question actually). I also asked a question (I believe titled "How to Heal Faster", but not sure) on here about nutrition/healing.

Have you been to a doctor? They can tell you when to put pressure on your injury better than anyone on this forum can. If you haven't, an MRI would be good too because it can tell you what part of the ligament tore, and if it is a partial or full tear. These will definitely influence the rate of healing. You might also consider PT for a week or two, if only to get some exercises to do.

Most of all though, go slowly. Injuries are tricky and its so easy to reinjure yourself.

I had an almost identical injury in November of last year. I don't know of any specific supplements, but I'm sure some could help. More importantly though, hit the physical therapy hard and keep up with it. I'm about 6 months out from my surgery, and my ankle will hurt some days and be great others. I was always very active and it's been rough not going full boar at everything. Just give it time. And then when you think you've given it time, give it some more time. Seriously, it'll just take a while. It can take upwards of a year to fully heal. In terms of exercise, I just started with basic walking. When I could bear enough pressure, I'd throw in some pushups, pullups, and planks. Once you can walk around pretty well, I'd try easing into yoga. That's helped me balance everything out since my non-injured leg took a lot of stress while on crutches and my injured leg had got pretty weak. Just go easy, don't push it too much, and try not to freak out over inactivity.

Zinc is incredibly helpful for ligament and tendon injuries.....put all my disc herniations on them during conservative treatment in hope of avoiding surgery.

Crashed my road bike during a training ride and broke my pelvis and scapula and sprained pretty much everything else. That was 5 years ago and I've finally found someone who has actually helped me get back to where I was. He's technically a physiotherapist, but not in a traditional sense. He's been trained in Gray Cook's Functional Mobility Screen and in about an hour identified some major strength imbalances and mobility problems. If you can find an FMS certified practitioner who actually knows his/her stuff, you could save yourself years of work and rehab. I found my guy through Gray Cook's website. Check it out.