Not knowing what to do, I asked my apartment's security guard for help in slightly panicked Chinese with the help of a Chinese-English dictionary app that my friend from Australia, Cameron had showed me when I was enrolled in Chinese-taught classes. After the guard tried to fix it a little with his bare hands and a broomstick, he turned to me and started making statements that I couldn't understand. We worked through the language barrier (true Beijingers speak Chinese in a different dialect than standard Mandarin and have a lot of terms only used in the area) and I figured out that he was saying that he needed some tools.
My roomates didn't have any, but I then remembered that I had brought my Swiss Army Knife that my parents had bought me in Middle school with me, so I rushed up to my apartment to get it and handed it to him. Carefully considering the tools it had, the guard took out the reamer and with a bit of straining, got part of the chain back onto the front gear. He then lifted the bike right-side up, grabbed a pedal with his hands, and told me to grab the other pedal to rotate the gear with him on the count of three. With two pushes, the chain snapped back onto the gear and was fixed!
After thanking him, I told him the original reason why I was trying to fix my bike (the wheel was still making noises); he grabbed the back wheel and frame, pushed hard with his hands, and fixed the problem in a matter of seconds. Looks like I don't need to take my bike to a repair shop anymore :)
If the guard had decided that I wasn't worth the trouble and not agreed to help, my friend hadn't given me that app after we got to know each other through a Chinese-taught class, or my parents had never bought me that Swiss Army Knife/I hadn't brought it along since I rarely use it, none of this would have happened. Thank God for modern day technology, multi-tool knives, the goodness of people, and help from unexpected places!