As much as I have read over and over again it is not an option for you..
This bird is in desperate need of another bird. All birds, especially budgies, are flock animals. People with only one bird spend a lot, a lot, of time with them and even then I wouldn't recommend anyone to get only one bird.
Depression kills, yes it does. But even, even if it did not, isn't it totally inhumane to keep an animal depressed, while you know there is a solution to their depression?
Your mother says it is our responsibility to care for animals we take into our home, but this is not caring for this bird, this bird is depressed and has no quality of life like this. So this sounds harsh, but this bird is not being cared for, and if we cannot make it so this bird IS being cared for, the best thing for everyone is to rehome this bird to someone who can offer what this bird needs.
Another bird will not be much more expensive. You can actually spend less time with your birds if there is a companion as they will keep each other company. They can share food and water dishes, and parakeets especially are social and easy to introduce to each other. Ofcourse there will be instances where they don't, but take into consideration how rare these are. And I am not talking about bickering, this is perfectly normal for budgies and isn't fighting.
Pellets can be expensive, yes. But have you looked around for cheaper prices? perhaps online ordering? Different shops? And honestly pellets are unnecessary for budgies IMHO. They can cause many problems, there is too much calcium, budgies are granivores, they are not formulated for budgies, will expand and take up water, among other things. Get a good quality parakeet seed, just simply a seed mix, no vitamin coatings, pellets, dried vegetables or other things, just plain old seed. Give your bird daily leafy greens such as broccoli, lettuce (no iceberg), silverbeet, sow thistle, chickweed, dandelion, and others, varying them as much as your can. And once or twice a week, either buy or make up your own eggfood. This is hard boiled egg, and bread crumbs, at a 1/1 ratio, mix them up into little pieces and feed to your bird, you can make your own bread crumbs out of bread, toast it and crumble it up and/or bake it low temperature in the oven. This is the food I have fed my birds for years and they are all fine. The thing about seeds being fatty and innutritious is wrong, most seed mixes have the same fat content as pellets, and no seeds do not have all the essential nutrients, that is where the leafy greens and eggfood come in. I know this an unpopular opinion but I believe it is right, you do not have to listen.
This is not to sound harsh or rude or make you feel bad at all. I am only trying to be straight to the point. I know you are in a hard situation right now and I really do feel for you. Regardless if if you listen to me or not, I hope that you can figure out a solution, and things get better for you and Blueberry.
