I raised a single hatchling in the bathroom. I used jam pot lids for food and water which were shallow. We used a painting tray with a mesh lid on it which suited fine - confined space so not too big and drafty, she slept on hay in the dip and the food and water went on the slope, and snuggled up with a little teddy.
You become mum really. I talked to it every time I went in, and as she grew we let her out onto the tiled floor with a few toys - toilet role tubes, and a tray of turf for pecking.
The tiled floor made it easy to clean up her poo - her name became Poopy of course.
She did really well, became finger tame, and eventually I selected her a buddy and the two of them went outside in a rabbit hutch run where they were surrounded by the other chickens. After a bit we lifted the lid and they went out during the day, but went home again at night, and that is how it went. This was the end of last year. She is now in the hen house and just lovely. Not so tame anymore but that is ok, she is thriving and happy.
It can be done - just be patient and you will both be fine!
Kate