I honestly think she was just angry. I don't see why she would think that she would get sympathy votes from fighting with Tim when she (probably) knows that he's one of the most popular HMs.
Agreed. If the argument were to gain sympathy or had an element of strategy it would not have been so explosive and emotional. Mikka is an intelligent, strong woman, albeit one with anally-retentive control freak tendencies, and as such if she wanted to milk something for sympathy it would most likely been done while she had some semblance of control via the diary room or through the gossiping to Ed, Jade and Maddie.