Does the manager know that you are bipolar? I would fear that your job may find some reason to fire you, so you may want to take them up on the offer before that happens. Mixed states are incredibly difficult to navigate. Time off can be temporary.

If your are in a mixed state, then you shouldn't feel ashamed to take time off from working. Try not to compare yourself to your brother, the dentist. I am suspecting that he is not bipolar. He does not have a medical condition that affects his daily functioning.

I think a lot of us can relate to having had expectations that we haven't met for ourselves. I agree with Justugh that you need to figure out your passion. Select a job in that category that offers less stress. Take the time off so that you and your pdoc can find a medication that helps control the cycling, and appreciate the extra time to look for a better match for yourself. Think of this as caring for your medical condition. If this were any other serious medical condition, we wouldn't even give taking time off a second thought. You have no control over having bipolar disorder except to treat it, so it is OK to let go of the shame you appear to feel.