How do I handle a friend who freaks out when the smallest thing goes wrong?

It sounds like she might be suffering from OCD and possibly anxiety (not necessarily a clinical case). You're going to have to confront her and tell her your concerns. If she can learn to recognize when something starts to upset her, breathing exercises might help http://www.holistic-online.com/remedies/anxiety/anx_breathing.htm she may want to try this. Good luck!