If I were in your shoes and I was still a kid without my own money, honestly at that point I would take the money out of mom's wallet, take the bird to the vet in a taxi, and deal with the consequences later. Your mom is not being respectful of your bird's needs.
I'm not advocating stealing from your parents. I'm just telling you what I would do to protect my feathered child's wellbeing.
Call the vet, explain your situation, see if they will see the bird pro-bono. Most vets will talk to you on the phone for free.