Sounds a tad painful.
You can see that from your description there is a loading issue. Without a full examination it is difficult to say exactly say what it could be.

The walking down hills - forward translation of the tibia which may in turn compress the fat pad at the from of the knee.
This is called Hoffa's fat pad and as physio0907 has suggested you should see a specialist.

In the meantime there is a little technique you can do, if when you walk, make sure that you emphasise pushing off with the ball of your foot and toes of the problem leg (don't walk with a limp that looks daft, just subtly push off. It should feel like you are propelling yourself forward), see how that goes over a day or two. It is a technique you can used which was suggested by Sahrmann and is quite good, worked for me. Failing that, a specialist will need to take a look. Most positions hurt in weight bearing if the fat pad is irritable, so best to get it seen too

Good luck

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