Sweeten the tea with honey. It helps with a runny nose, cough, and congestion. I went through this recently, too, minus the chills.
Soak in a hot bath for 30 minutes, then get out and bundle up. I do this anytime I feel a fever coming (chills, aches, etc.). Fever is your body trying to kill a virus, so I save some "body energy" by soaking in a hot bath and raising my temp that way. Get the water as warm as you can tolerate without burning your skin, and stay in for the full 30 minutes, even if the water cools down.
A hot shower would work, too, but uses a lot of water. Maybe a sauna if you have one nearby.