Is "what am I gonna do?" an actual question? or she is just saying to herself?

Rebecca

She's not talking to herself, but it's clear that she is not necessarily looking for an answer to her question. It seems she just wants to talk about a situation that is stressful to her, and perhaps just needs someone to listen to her (and not to provide a solution). When people ask "what do I do/what am I going to do," it's often a precursor for a rant about a stressful situation, and not a real question seeking an answer. Of course, you have to look at context as well when deciding the speaker's intent in using this expression.