I find Cataclysm DDA to be the most annoyingly realistic cold simulator ever.
Yes, Nyquil does make you tired and sleepy. Also, coughing while trying to sleep means you are getting a lot less rest than you should.
There are two ways of dealing with a cold.
If you are bunkered down and have supplies, use Nyquil and sleep it off. Indeed, you’ll probably wake up tired, and frying a couple of pieces of meat, boiling a bottle of water and taking one Nyquil will get you back to dead tired.
Eat well, keep yourself hydrated, keep all your body parts warm while sleeping and you should be fine in 4 days.
Without Nyquil it should be like 7 days or so.
If you can’t afford to be lethargic for days at an end, use Dayquil.
I only use it in emergencies. It does not make you sleepy, and as such it’s priceless. You can never have enough of it stashed.