For what it is worth: My guess is that it is a personality style/personality disorder.
It is really hard to know how she is in the real world, because this type of environment in and of itself creates understandable vigilance and distrust/suspiciousness, but if she is consistently like this outside the BB house, one would have to wonder about a paranoid personality style. The things that would make that possible are her excessive sensitivity to comments and actions of others and the tendency to interpret the actions of others as deliberately threatening and demeaning to her, and not being able to let it go. (eg. her comment to Rachael about being the poorest sport in the house after Rachael said "thanks beaubeau" or her comment to Kaysar about his not respecting women).

Again, being in this setting naturally creates a sense of mistrust so I may be way off base, but a paranoid personality tends to be easily slighted and quick to react with anger or counterattack, and is distrustful and suspicious of others. At their best, they place a high premium on loyalty, fidelity and working hard to earn and maintain loyalty, but at their worst they doubt that others will be loyal or faithful to them. They often suspect (on the basis of little or no evidence) that others are out to harm them, and may retaliate at any time angrily and with aggression. They often feel righteously indignant and unable to see their own role in conflict. They are untrusting, bear grudges and are unforgiving of insults or slights. At their best, they can be self-assured and confident in making decisions, good listeners and observers, sizing up individuals before entering into relationships with them and be assertive. At their worst, they are suspicious that the motives of others are malevolent and intent on harming them, and believe that they are being exploited or deceived and respond with aggression and even litigation.

Of course, even as I write this, I am thinking that being a contestant in Big Brother would be a sure way to at least temporarily create this style or make it more entrenched.

The other personality style that could be there would be a narcissistic style. They have a grandiose sense of self-importance and expect to be recognized as superior. They react to criticism with feelings of rage or stress, are interpersonally exploitive, taking advantage of others to achieve their own ends, have a sense of entitlement and require excessive admiration, have a preoccupation with fantasies of unlimited success, power, brilliance, beauty or love (?Cappy idealization??), lack empathy, are often envious of others or believe that others are envious of them, and can be arrogant or haughty in behaviour or attitude.

That's my abnormal psyche 101 guess for what it is worth.