Why does my voice get deeper when I am sick?
This is a WAG, but a good one, I think.
Conceptualize your vocal chords as guitar strings. Thicker, heavier strings produce lower tones.
When you get sick, you can get inflammation of the vocal chords. This makes them thicker and heavier, making the tones they produce lower.
Coincidentally enough, I asked this very question a couple of months ago. Here’s the link.