I had the same issue as you in December when I crashed my car, which has now been replaced with a 500 dollar station wagon which is covered in bike stickers and soon will have a thule rack a top, but I digress.

I had commuted before when I lived with my parents but it was totally different, I used my touring bike with a pannier and had a relatively safe commute. This winter though (and now) I was living with my grandmother in an urban area with very narrow and busy streets with motorists who were not interested in my saftey. I was also dealing with train schedules that would leave me banned from the train until before (like 630AM) and after rush hour. You'll adapt to it very quickly and it will get much easier. I felt a bit overwhelmed because I had to carry stuff for school and work and I had to be mindful of the train schedule and stuff and I was worried about my fixie getting stolen, I couldn't use panniers as they would be stolen in a second, etc. But by like day 3 I had it down, I had figured out how to dress so I wouldn't have to carry a complete change of clothes for work but still be able to pedal the bike without going to work smelling like a locker room or freezing to death. I got really fast with a U-lock and chain, I got more confident with my fixed gear, I got very organized in packing the day before. It seems tough but you adapt really quick, good luck to you!