Here you have a character. We will call her Helena.
I like this characterization, and I think it's part of a greater point. Setting up realistic flaws and responses can actually do a lot of the work of thinking up the interactions between the character and her companions later on.
Like Helena. As you said, people think she gets angry at the drop of a hat, and holds grudges - and she's too proud to apologize. This naturally leads to greater speculation and depth to her character (for example, is she constantly getting in trouble by shooting off her mouth, and so forth?), and flows into various situations (such as accidentally getting herself beaten up because she couldn't keep her damn mouth shut when the local strongman made a snide remark). It also probably leads to other bits of characterization - is she one of those people who seem immune to consequences (the types of idiots who run red lights and repeatedly rack up tickets)?
Sorry if that sounds kind of incoherent.
She can have lots of bad ones, as long as you show them affecting her and the world around her with some psychological realism.
Oh yes. The character I'm thinking of here would be Cersei from GRRM's books - she's clever, but impulsive, inclined towards cruelty, impatient, and not the type to step back and examine the greater consequences, which gets herself and others in trouble. You can get a lot of mileage from a character whose main flaws are they're careless, or ignorant-but-don't-care-about-it, or impulsive, and so forth.