i'm not sure i'd hop on a fixed just yet. huerro's right, talk to someone in sports medicine. a traditional freewheel bike would probably be a good bet until your knees get strong enough. your knees get used/abused quite a bit if you're riding a fixed every single day. when i was working as a messenger there were times when i'd have to ice down every night, and i have no history of knee problems. (then again i was riding upwards of 50 or 60 miles a day with no brake). if you ride less you may be okay.

i also spoke with an older (40 something) messenger who said he'd been riding a fixed his whole adult life and his knees were shot now. he probably rode way more than the average rider, but knees are important, and you only get two until nanotechnology catches up.

again, i'm not in medicine so you should talk to a professional.