FTBgirl i really think you need to speak to your mum about this whole animal thing- i agree with pica_nuttalli in particular.
Have a thorough talk with your mum- although you seem to be aware that you have so many animals now that looking after them properly/well is becomming very difficult, your mum does not seem to realise this problem.
Speak to your mum about this situation as the situation is not good- you won't be the first one who has had to adress stuff like their to their mother either. For example, my mother keeps on nagging me to buy her some goldfish for her pond, but i refuse to let her have any goldfish on the grounds that the last ones she had, she let them starve to death. So basically, sometimes you have to raise issues like this with your parents even though getting such points across to them can seomtimes be difficult and fustrating.
You have a responsability to raise these concerns to your mother, as by agreeing with your mother about taking in the birds, you are at least partly responsable for them entering your house under your care.
You must spend like every day cleaning out your pets housing right now, with all the rabbits and fish and now birds, which must take a great deal of the fun out of having such animals. I only just happily manage with my 4 fish tanks and 3 pet rats, i can't imagine how much time you must spend every week cleaning out loads of hutches and cages and aquariums and stuff etc. And then you have to have all the other time needed to be spent spending quality time with the animals and giving them the love and attention they need- if you are looking after all of these animals well in these respects, i wouldn't be surprised that you hardly have any free time to yourself to do with what you want with.
... ... ...
You're only 14 right now, and i expect that you do a great deal of the looking after for these pets, i think your mother is irresponsable in letting you have so many animals at this age- think about it this way: What are you going to do in the near future when you (might) want to go to Uni or college and you can't be there all the time to look after all the animals? What about when you go into full time work, are you really going to have the time and energy to keep up on all this maintanence after working 8 hours every week day and want to go out at the weekend too? What if when you want to move out of home, no landlords will let you have animals in your rented accomodation? Who's going to look after them then?
Can you really trust your mother to clean out dozens of rabbit and bird cages and aquariums every week and keep up on all the other maintanence and give the animals all the time needed to be spent with them to dote love and attention on them etc?
The problem with situations like this, is that more than often you can only rely on yourself. Keeping any sort of pet takes a lot of responsability and at least a fair amount of time (and not to mention money too)- you might be at school spending a fair amount of time there and working hard, but as you grow older your schedule will become so much more hectic and harder if you really want to do stuff in life and go to great places etc.
I don't expect you to be able to really contemplate this kind of stuff right now at your age, however i think out of all people your mother (being the adult) has been the least responsable person in this whole drama/situation. You really need to speak to her.
Anyhoo...
I'm sure you are enjoying the new birds though right now, did you do any thorough research into keeping finches before you adopted them?
edit: sp