Hi, Mandie. Curtis Park here! Welcome to BF.
I'd suggest going to the Bike Biz on Freeport (across the street from CK McClatchy HS) and checking them out. They have some nice and relatively inexpensive SS/FG bikes.
I also think City has Madisons and Bianchi Pistas in stock. Worth taking a look.
I don't know if you've ever ridden fixed before. There's nothing magic about it--it's just a single speed bike that cannot coast. You can brake with your feet, but I'd still get a caliper brake or even two.
Good luck!