How can i reason with my mom to let me get another atiel?

i am 14 years old and we used to have two atiels but one died from egg binding and we were positive my sister was allergic to the other one (it turns out she just has a chromosome imbalance) so we got rid of her for no reason. when i was 10 i got a hamster but he was so disgusting (because his are huge and he smells gross and pisses on things) that my mom said "why don't you give him to your sister" so when i was 13 i gave him to my 10 year old sister who loves him a lot. i really miss having a pet but the hamster truly sickens me because he is so gross and i miss my birdies so much! my mom won't let me get a pet because she says i won't commit to it but that's just because of the whole hamster thing i loved the birds. what can i say to her to make her at least listen? i get 40$ a month for babysitting and that's not going to change anytime soon. i also have a new job at a rock climbing wall but its not a regular job so i don't know how much money i will make because it depends on how much i work. she won't even listen to me. she lets me get a belly piercing but not a pet bird?! how can i convince her? i really will take care of it like i took care of our other birds. (which was well by the way.)