I had a horrible cough for 3 weeks in December, and I am also someone who rarely gets extremely sick. Usually I get better within a few days, this was just painfully awful!
So, the home remedies I tried that worked:
1) Cayenne pepper (just a pinch) in hot water. The warm tinglies in my throat from that kept the cough controllable. Can add this to tea or tea with honey if you want, but you won't really be able to taste the difference.
2) To sleep - I couldn't sleep because I was coughing so much. I made a concoction of hot water, honey, a whole fresh squeezed lemon, a pinch of cayenne pepper, and a shot or two of either whisky or rum. The lemon for the vitamin C, the cayenne for the tingle, the liqueur to relax my throat, and the honey to make it all taste good and go down smooth. This gave me 4 hours of sleep at a stretch.
Good luck, I hope you don't cough for 3 weeks straight!
Oh, and one more thing, cough drops only made this cough worse! They work while they are actually in your mouth, but after they are gone the cough was worse than ever!