This little chick sounds just like a chick I had last summer. It was painful for us both when she would try to poop because she would scream in pain each time she squatted. She didn't grow, except for her wings, which overtook her tiny body, becoming much longer than she was. She looked like a fly instead of a chick.
I treated her for cocci, and that didn't help. I treated her for constipation, and that didn't help. She peeped non-stop. I knew she was in a lot of pain. At one point, she greeted me one morning all feisty-like, and I thought she had turned a corner during the night and might make it, but she got worse, and each day she got even worse.
By the end of her first week, she just laid there, not eating or even standing or walking. I euthanized her to stop the pain, hers and mine. I had other chicks in a brooder outside, and this chick was the only one I had named so far. Sunny. She was my first experience with a FTT chick. It's just heart breaking.
Try smoothing coconut oil on your chick's vent. It might help it be less painful when she has to poop. Have you tried vitamin drops like Poultry Nutridrench or Poly-vi-sol? If your chick is eating and drinking, there's hope for her, but I think she probably has genetic abnormalities that cause internal problems, and there may be something wrong inside making it hard to poop. You could try some mineral oil and see if it helps. Put a little in a tiny cup and hold it under her beak for her to sip. If she won't, take an eye dropper and squeeze the oil just into the side of her beak, not down her throat or she could aspirate it. If she had really bad pasty butt, she could still be plugged up on the inside.
Also, try squeezing a little mineral oil inside her vent, careful not to go too far. if she's plugged up, it could help to loosen things from the bottom end.