I do have a question about obtaining a hearing dog for myself.
When I was a teenager my parents tried to get me one but they had to be put on a "list" and were told it'd take up to a year maybe more to get me one. I forget what organization they went through it's been over 12 years since I even looked into getting one. I currently have a pitbull that I've tried to train as my hearing dog but she's too hyper to train in that regards other than to sit, stay and come. She's protective and lets me know if there is someone snooping around my home or if someone is at the front door but as far as alerting me when the tornado sirens go off, or when the phone is ringing...nadda.
I know labs are often used as hearing dogs but a pitbull?
There's no reason a pittie couldn't be trained as a hearing service dog. In fact at a recent HLAA conference, there were several service dogs there. One was a white pittie that I just fell in love with, she was so sweet. Very dignified looking and not "cute" at all; just the picture of professionalism. Lovely dog.
It will take a LOT of work on your part, ideally with a professional trainer for starters. Because some people have a negative opinion about pit bulls, you will have to work extra-hard to make sure she is entirely calm around people and 100% responsive to your commands and needs.
Generally the hearing assistance dog placement outfits will NOT place a hearing service dog with someone who already has a dog as a pet. It interferes with the bonding necessary. So - basically, it's a question of working with what you have.
Have you taken any obedience classes at all with your dog? You could look around and see what's offered by your city or county. Or look up professional dog trainers in your area for one-on-one training. A pro could evaluate your dog for trainability. If she knows sit, stay and come, that's a good start.
Does she walk well on a leash for you? Do you make her wait a few seconds for her breakfast and dinner? (That helps in impulse control: put the food down, say or gesture "Wait" and give it a couple seconds before saying or gesturing "OK." ) A dog with good impulse control is easier to train.
Also google "Clicker training" and take a class in it if you can. It is amazing how quickly dogs can learn through that method.
Good luck and let us know how it goes.