I think you've got it, you've finally chilled out, gotten enough sleep, and allowed your body to use the energy it needed to finish cleaning house. I've been sleeping on average 12 hours recently, and I definitely notice a bit of detox.
So it's not so much that it's making you sick...the body is performing perfectly at all times relative to the conditions you are presenting it with. So if being "sick" with a runny nose, coughing, etc. is what your body needed to do to expel toxins, that's a good thing! :D