I would argue that the conclusions that you reach rest on a misconception of free will. That's understandable, though, as the historical debate over various conceptions of free will. If we're presuming the conception of free will as the "little unmoved mover" then I think we can dispense with that immediately. No such thing.

Instead, let's consider the definition of free will in its most general: the ability to choose between different possible courses of action. A compatibilist would say that your bipolar disorder wasn't some outside force that made your choices for you despite some real you underneath too helpless to behave otherwise. Your bipolar disorder isn't something that you have but something that you are, just as it's incorrect to say that we are at the mercy of the chemicals and neurons in your brain. To the materialist, you are the chemicals and neurons that are your brain. When your bipolar disorder was manifest, you did want to act like that and you did choose to. There's nothing inherent to the idea of free will that it must be orderly or rational. Fortunately, therapy and medications helped you to regain order through steps you had chosen to pursue.