She has some kind of medical problem. It has nothing to do with the cold.
I don’t know your story, how many chicken you have, whether you had a flock when you got her, or if you got several chickens at the same time. If you happen to have more than one, is she the only one acting this way?
My first thought because of the timing, four weeks since you brought her home, is Coccidiosis. Treating her with Corid might be a great thing to do. Start today.
If you already had a flock it’s possible your flock could have flock immunities. They won’t show any symptoms but they can be carriers that infect new chickens. Coccidiosis is one possibility but there could be others. When chickens are sick they act that way. Are you seeing any other symptoms, runny noses, watery eyes? Have you seen her poop, that can be a good clue?
Is she molting? Most of my chickens act pretty normal when they are molting but I have had some fast molters (they drop a lot of feathers pretty quickly) that sort of act that way. They spend extra time on the roost in the morning or set around kind of hunched up like they don’t feel really well. Different chickens are affected differently by the molt.
It is possible she is injured. She may have banged into something when she was flying down from the roost or maybe injured herself trying to get away from an amorous rooster or if she panicked when losing a pecking order fight. She may have swallowed a nail, screw, or sharp piece of glass that punctured her gizzard when she was trying to grind it up.
Have you checked her for mites or lice? Worms? A heavy dose of parasites can cause that behavior, though that sounds extreme.
At 16 weeks she is probably too young to be egg bound or have internal laying.
It’s really hard to diagnose over the internet. Even when you are looking at them it can be challenging. In addition to the Corid, I’d try feeding and watering her. You can get electrolytes or nutri-drench, a lot of people use those. Sugar water can help. I’ve used hummingbird liquid. The idea is to get some moisture into her so she doesn’t dehydrate, plus give her something to raise her energy level so she feels like eating and drinking on her own. I put a drop of liquid on the tip of her beak with a medicine dropper and let her drink. If you try to force it down her throat you can drown her.
Good luck! This can be challenging.