Parents won’t let me take SICK parakeet to vet?

I think my parakeet has a respiratory infection. It does not look extremely dangerous/severe at this point (he is breathing heavily, occasionally puffing up, tail quivering BAD, and maybe a little bit of seed stuck in one nostril), but I am afraid that if I do not get it taken care of now, it will get worse and the vets won’t be able to do anything for him. My mom keeps saying “It’s just a BIRD. So what if he dies? It will be sad, but that is just what happens.” My dad told me that he would help me out with the vet costs but that animals can usually get better by themselves so I should wait a few days. I have them to the point now that they will let me take him, but they are extremely reluctant and think it would be really stupid.
Should I wait?
What should I say?
What is the normal cost to get this taken care of? (I plan to take him to an avian vet)
HELP!

What are some ways to prove I can take care of a parakeet?

I need to get my parents to let me get a budgie/parakeet. Any suggestions to impress them? I really want a parakeet.
- BudgieGIrl

Are parakeets hard to take care of and would you recommend it? Can they talk?

i realy want one …… My parents said maybe so im trying to convince them by finding positive facts about them on the internet!
- SuNsHiNe: )

my parents say that parakeets are to noisy smelly and messy and also hard to take care of?

i have been trying to bribe my parents to let me have one so if you have had expeirience with them please answer my question.
- zoe B