Absolutely not.
If you were to experience breakouts every time you drink coffee (which you don't according to your post) it would be because of an allergic reaction to the coffee or an ingredient in the coffee itself.
Contrary to common belief, there is no such thing as a food that makes you break out. However eating healthier foods may improve the look of your skin or do something of similar importance ( help to de-stress.)
Although I experience no breakouts from coffee, I do find myself more alert and many times fidgety and anxious when I drink it. The side affects of caffeine can be useful when your pressed for time or in the mood for a pick/wake-me-up. However, when you ingest something that makes you more aware and stressed, during an already stressful situation you relay twice the stress upon yourself. Perhaps you should try a caffeinated tea to help to relax. Feeling daring? Mind over Matter. Try non-caffeinated coffees, teas, and sodas during the evening to help get better sleep and help to start the day off and wake up easier (perhaps not needing coffee at all in the morning). Or get a friend to sneak you non-caffeinated products and see if you really know the difference between the two. If this doesn't work try breathing exercises or yoga before bed and/or first thing in the morning. (I know this is easier said than done, but don't take yourself too seriously, and Relax, Live a little! all road blocks will smooth themself over with time.)
So far, we've cleared up the breakout dangers. But the only thing coffee may induce upon you worse than breakouts may be addiction. Watch the caffeine intake and you should be fine. Don't get me wrong, I love a good Frappucino almost every summer morning, and sometimes during the winter, along with an occasional cup "light and sweet."
I hope this clears up your questions, and helps you with whatever stressful situation your experiencing. PM me if you have any questions.
All the best,
Amber