I'm an avid cyclist, once I learnd how to ride I never stopped. I have had 5 knee surgeries and ride fixed frequently. Getting a proper gear for your terrain and riding aware is all you need to be safe and comfortable riding fixed. I ride 46/15 on my '86 Miyata Pista, and my home-built Marin SS MTB I ride 34/16. I have managed a couple bike shops, used to collect high end vintage race bikes and have built more bikes than I care to remember.
Knee pain and riding fixed do not go hand-in-hand. If you are having knee pain, first thing to check is your pedals, often you are not aligned properly. Second, you might have too tall of gearing. If you ride stop and go city traffic, lower your gearing. For flat city riding, consider a 44/16 or 42/16. I don't worry about gear inches, just know what gearing you use. I don't have to worry too much about stopping on my dail commute, and I tend to stay off busy roads, so 46/15 works well for me.
To the OP, with your new bike be sure you set it up for proper riding position. To low of a seat and to tall of a handle bar combined with tall gearing will wreak havok on your joints. Leg extension should be about 20* from straight at the bottom of the stroke. Another factor to consider is crank arm length. I ride 165mm cranks on my fixed, makes a huge difference when trying to decelerate or when out of the saddle.
Also, clipless or toe cages should always be used when riding fixed. This allows you to apply back pressure on both pedals evenly, rather than just on the up stroke. Having a short Q-factor seems more comfortable as well.
Ride safe and keep the rubber side down! Btw, I recommend Vredestein Fortezza Tri-Comp tires, good wear resistance, high pressure rated and super grippy without much rolling resistance. I love 'em, been riding them for 5+ years! They come in colors too!
My Miyata Pista...
-Xander