I think the allergies depend on the cat!

I have three. With one of them, I've learned the hard way never to pet her and then rub my eyes.

I'm pretty sure if I put a sweater on any of my cats it would be off in less than a minute. I have one that loves collars though.

I bought a blanket coat for my cat years ago. online store i think. he was larger than the mamma cat i have now but she uses it when it's below zero outside and she wants to go walking. On a leash!
it has velcro that closes around the neck and a band that closes under the tummy area. these coats are mostly made for dogs. but it works

My one female cat is always cold too. I am forever finding her under the blankets in my bed or laying on one of those big clunky hot water radiators even before her haircut. We got her and her sibling shaved down before Xmas. Boy oh boy there is so much less hair. I love it!!!!

If the sweater for your cat doesn't work out, you may want to try Linda McD's (Elisabrat) suggestion of an electric blanket. Or try a heat lamp or even a regular bulb above kitty's bed. My DH made a special bed with a heat lamp above it for a very old cat we used to have who had very stiff limbs. Oh my, did she ever like that! She always had a blissful look on her face while curled up under that heat lamp. A week ago I set a stereo on a table temporarily and by chance it was directly underneath the bulb of a floor lamp. Our Siamese quickly learned this was a nice warm spot. She laid for hours on the stereo directly under the bulb. She had that same blissful look on her face. She was devastated when the stereo and lamp were taken away (we're moving).

Maybe if you can give your cat a nice warm spot, she won't feel the need to sleep with you. If she persists, you can always close your door, knowing she has a warm spot to go to.

Poor kitty. Why not try a dog sweater.

I made a small fleece blanket which i put on the top of my chair(simon sleeps there) and I have another one in the chair in my BR. He also sleeps directly on the registers when the heat on , but he would never keep a sweater on no matter how cold he gets. My older female use to climb under the throw blanket on my bed.

Better have plenty of Neosporin if you think you can get a sweater on a cat.

mY OLDEST IS 18 YEARS OLD AND HAS SOME ARTRITIS IN HER HIPS WE LET HER HAVE A SQUARE OF THICK BATTING AND SHE LIKES THAT TO KEEP WARM. THEY HAVE A SIMILAR PRODUCT AT THE PET STORE THAT WARM THEM BY THEIR BODY HEAT. LOOKED LIKE BATTING TO ME. WE JUST BUY THE CHEAP TYPE FOR THE CATS AND I MAKE BEDS FOR THEM WITH IT ALSO. WE ALSO TAKE TWO STORAGE BINS AND PUT ONE UPSIDE DOWN ON THE OTHER AND COVER IT AND PUT A PAD IN IT. THAT GIVES THEM A CAVE THEY RALLY LIKE. THEY WOULDN'T USE THE ONES WE BOUGHT AT THE STORE THAT ARE ALSO SCRATCH POST.BUT THEY WILL USE ROPE SCRATCHING POST. CATS ARE FUNNY LITTLE CREATURES. BUT WE LOVE THEM.

when i brought home tenzing at only 4 weeks old, he was always cold. during the day he stayed in my pocket for warmth and during the night i put almost boiling water in tupperware, with a handtowel tucked around it and he slept all night on that. the water stayed hot all night and i kept it in the corner of a box so he wouldn't roll off. he stayed cold all his life and always slept with his head on my shoulder, under the covers. it went on that way until he died at 18 years, BUT, WHEN I TRIED TO PUT A SWEATER ON HIM, HE LAUGHED HIS BUTT OFF.