All fixed gears are single-speed, but not all single-speeds are fixed gears. (The first part is not even necessarily true--there have been multi-speed fixed gears.)
OP, a single-speed could have been converted by simply removing the derailleur and putting the chain on a single cog in back. My point is that it's hard to tell you how to get somewhere without knowing where you're at. The proper route is to get a track or fixed/free flip-flop hub/wheel, but maybe you already have one.
Not wearing a helmet makes me more aware of my surroundings. I find myself anticipating the hardness of concrete 50 or 100 feet in front of me, it's almost a zen-like connection between my face and the pavement.