HI Narcissus and thanks for your informative post. You did not actually say what you were doing when the injury happened. Sometimes that information is useful so we can understand the direction of forces applied to the area at the time.
Your doctor is pretty correct in 6-12 weeks (and more like 12 weeks) being standard for this type of injury. The issues of the ligaments are poorly supplied with blood and so healing is slower than other areas. Additionally if you want to keep a tight ligament structure you don't want to be stretching it too much to soon in that process. This is why commonly a knee brace is prescribed following collateral ligament injury combined with complete rest. Exercises as such are not going to help although if it is pain free stationary cycling should be OK, as would freestyle swimming (avoid breaststroke). I have found it useful, both personally and with clients, to take some glucosamine sulphate supplements which seems to assist the rate of healing (could be direct or indirect effect on the bodies healing functions). In some cases it was only after 7-10 days of taking the additional 'food' that my pain resolved completely. Another option would be to do some work on the footbar of a pilates reformer (see if there is a local pilates studio with equipment).
So the take home message here is to back off, do activities that do not cause rotational or lateral stress on the structures, and perhaps take some additional supplement to assist the healing. If the pain does persist you can get someone to do deep cross-frictional massage to the injured structures, as well as some deep tissue massage to the hamstrings, as that can also be of help if there is some persistent pain.
Let us know how you get on and we can give some more input.
regards
PhysioBob