I had a really similar problem...****ed up my knee at some point last winter, and took serious time off cycling for most of the year. I was getting pain whenever I rode much in my left knee, causing problems with my profession (messenger). When I got back into town after travelling for most of the year I finished up the fixie wheel I'd been riding before I left, and threw together a bunch of spare parts on a classic old 10-speed frame (prismic foil-lined tubes and a skull and crossbones on the head tube). Bingo, instant fixie, which I've slowly been upgrading ever since. The most important one has been a new seatpost...the old one was one of those 10-inch bastards from the 70s and I couldn't get the seat high enough. I started getting crazy knee pain again, and decided to stick to racers while working (carbon, ultegra, roadies) and sticking to spinning/low ratios and only used the fixie for errands and commuting to school once a week. A 3 km stretch to school and back had me in horrible pain, I'd even have to wear a leg brace for the next day or so (they do help). Even if I used my brake for most of the stops, it was kililng me, much more so than riding 10 times as much daily on geared bikes. Since I got the new seatpost and added a liberal few inches onto the old height I've built up much better muscles and ligiments in my knees and the problems have all dropped away... Using the fixie at work now for the winter and loving every minute of it.
Seat height is so important for so many reasons. I've had professional fits...all poppycock as far as I'm concerned...ride around with a wrench and don't stop fiddling until you're perfect. Far as position, height, angle etc are concerned, only you can really be the judge.