For about the last month now, I have been a total zombie. I do sleep at night and wake up feeling ok, but as the day goes on I realise that I am exhausted. I have no energy and find that I really struggle to motivate myself at work.
You have the classic sympotoms of fatigue. You suffer from a lack of energy, drowsiness and apathy (indifference and a lack of motivation). This is not surprising, as you are clearly exhausted. Fatigue can be caused by many factors, from lack of sleep to stress. Get some rest.