knee pain is something almost every fixed gear rider must get through. it is simply due to extra stress on the knee, and all you have to do is take a few days to a week off the bike, get back on and ride the same amount of time, try again, and repeat untill it goes away. muscles, cartilige and other stuff builds up around your joint to help cushion, lube, and make the knee work properly. its just like working on specific muscle groups, but with your knee.
putting a brake on takes away some of the extra stress. your knee will be weaker, but it will most likely stop hurting instantly. however, if you ever get on a track bike or even start sprinting really hard sometimes the knee will start hurting again, because it is not ready for the stress.