I understand your concern. 20mg fluoxetine does not usually cause that much drowsiness which you have mentioned, to the extent of affecting your work / initiative. The reason for the same needs to be evaluated further. Please discuss with your psychiatrist about the problem. You seem to be suffering from residual depressive symptoms is what I feel. Information regarding your sleep, hunger, energy levels and concentration at whatever you do would be more helpful to decide on the severity of your present condition. However it is easily manageable with appropriate treatment. Some counselling sessions along with medical help also might be useful for you. I would also be more than happy to help you with that if you are looking for second opinion or online assistance. You can directly consult with me through Practo as needed. Online chat consultation is also available.

I would suggest you to consult a psychologist.