It sounds to me like a water fast is just the ticket. If you feel quite down after your cold, eating is the last thing you should be doing. As a Natural Hygienist, I see the cold as a remedy for toxicity in the body. I would be resting/sleeping as much as possible to allow the body to complete the cleansing process and taking my cue from when my appetite and energy returned.
If you use up the extra energy on work and getting things done, you might be doing your body a big disservice.
Good luck on your fast! :)