Zeig,
It depends upon which ligament you injured (sprained). The collateral ligaments on the medial and lateral side of the knee will heal on their own, as long as the injury was not a complete rupture.
However, the cruciate ligaments, inside the knee joint, to not heal themselves. Since they are bathed in synovial fluid, they do not heal on their own. If the ACL is incompetent, and the patient cannot compensate for the instability, then surgery is usually offered.
So, again, it depends upon the ligament injured and how badly it was damaged.
A medial collateral ligament (MCL) sprain is usually treated with rest, ice, compression, and elevation when it initially occurs. Then, physical therapy for range of motion is started, as soon as the patient can tolerate it. A hinged knee brace is used if there is opening of the joint with valgus stressing of the ligament. The knee brace is discontinued as soon as the patient has regained full range of motion. The muscles around the knee are strengthened.
It is very common for the quadriceps muscles to become weak after a knee injury, and this can occur very quickly. So, it is not surprising that your knee gave way after the injury. The quads are the main postural muscles of the lower extremities. They are responsible for keeping you upright and standing.
At two months out, it is basically up to you, as to what you want to use. Most patients will use ice before and after activity, or for acute, sharp pain. Heat is preferred for soothing soreness, such as in the evening or when relaxing.
You need to make sure that you have full range of motion of the knee. This includes full extension. Lack of full extension can also make your knee buckle when stress is applied to it.
Then you need to really work on quad strength. But, do not forget the hamstrings also.
You may want to use a light neoprene knee sleeve. You do not need a heavy ACL brace. Just something light to provide some warmth and comfort to the joint. It is your own muscles that are the most important stabilizing structures in the knee. So, again, an expensive, heavy ACL sports brace is not needed for an MCL injury.
Once you have full range of motion and strength, if you note that you are still having problems, you may want to have the knee evaluated by an orthopedic surgeon. Also, if you are unable to get full range of motion (especially extension), you may want to be seen sooner rather than later, by the orthopedic surgeon. Occasionally, inability to obtain full extension can be a sign of a torn meniscus.
Good luck. Hope you get back to skating and fencing soon.