Supposedly Sick Bird?

My pet parakeet was always a little chubby, but recently she has lost that little fat line on her stomach. I have been trying to switch her diet to pellets for a while, feeding her a mixture of Kaytee's pellets and seed, but she only picks out the seeds.

She's a lazy little bird that only flies to her foodbowl to eat. Today, she was sitting very still with almost no movement at all. She was looking normal, but when I checked on her again, she was sitting hunched over her favorite toy with her tail slightly bobbing.

I moved her to a warmer location, but she seems to be overheating. Her eyes, nose, and vent are clear, but her poop seems smaller these days. I am unsure of whether she is sick or not. She is a 4 year old obese female parakeet that is usually inactive.

My parents forbid me to bring her to the vet unless she is on the brink of death, so if she is sick, please tell me home remedies to cure my bird. Thanks in advance! :]