жопка is diminutive of жопа ‘ass’.
у меня жопа means ‘I’m in a difficult situation’ / ‘I’m in deep shit’.
у меня жопка is not common. It is an occasionalism. Maybe, it implies a not-so-deep shit, or, maybe, the author wanted to soften the rude word.
что-то (literally, ‘something’) means ‘for some reason’ in colloquial speech.
со своим ‘with mine’ usually implies meaning ‘with my boyfriend’ or ‘with my husband’.