Is this from, "The Yellow Birds"? It sounds familiar. Anyway, there's a lot going on here. "To get fed up", means that a threshold has been passed resulting in a demonstration of emotion. For instance: I got fed up with the constant pounding and yelled at the construction workers. I got fed up with her complaining and told her to shut her mouth. In this case the author is telling us that he got "fed up" over something unimportant -- that he over-reacted to a situation. The clue is in the preceding sentence, "I was still young enough for the weak mannerisms of rebellion." The author practiced these "weak mannerisms of rebellion" from when he was twelve until it culminated in his "getting fed up over nothing" and leaving in a taxi cab.