First, get you one of these:
http://www.amazon.com/AAA-Piece-Expl...r+roadside+kit
I always carry my phone, spare spark plugs, jumper cables, a jack, tire iron, doughnut, spare bulbs, a first aid kit, some basic tools, oil, transmission fluid, washer fluid, tire gauge and kitty litter in my car, just in case. When I got my first car, it was sooo old. Every month, something broke on it, much of the time, leaving me stranded, once, even in a place with no cell reception

Have an emergency contact in your phone. Oh, yes, and get a gas can. Forgot about that. Your anxiety is justified, even a better mindset than being cocky. Being a cautious and careful driver will help to keep your insurance rates nice and low.