Thanks so much for your detailed explanation.
Here's a drawing of the swelling/worst part:
In the first 2-3 weeks, the knee gave way a lot even on a flat surface and even after the pain had subsided. It no longer gives way now though.
Would strengthening also reduce swelling?
Well, I couldn't move about at all for the first 10 or so days, so I had to cycle (very slowly) to work. I had to use a lot of my right leg to do the walking. As with jogging, even now I can't jog very far (for about 10s) - it feels a bit painful if I keep on going. But mostly, it just just feels funny if I keep on jogging. The pain isn't excruciating enough to stop me going further, so I'm not sure if it's the weakness or something else.