You need to talk to your mother about the importance of establishing a relationship with a veterinarian for preventative health care for your new family member.My mom is just worried because we are new owners and if the bird falls ill from the first day, it might not get better? or not. but if she is sick some time later we would take her to the vet.
The problem with birds is, often, by the time you notice they are ill they are almost dead. So at that point rushing about trying to find a competent avian vet is almost impossible. Worse the local veterinarians are usually not competent with birds. You need a bird specialist and a good one and those are hard to find at the best of times. It's impossible to find if you are in an emergency situation where time is of the essence.
The way I bring a new bird into the family is I setup an appointment with my avian vet and give them all the new bird's prior vet's information. So my vet can responsibly transfer care and any medical history. This also gives me another data point on whether I should purchase from this breeder.
Then arrange to pick up the bird from the breeder just prior to the appointment. I then swing by the vet's and get the bird a baseline checkup. At this point weight, baseline blood tests and fecal samples are taken. Any wing trimming, beak trimming, nail trimming is also done.
Later I train all my birds to allow me to do this grooming but at the very beginning you want the vet's office to do this.
The other thing I do when bringing a new bird home is I create a quarantine area. This area is separate from the household it's also quiet and attached to a bathroom. So on my way in and out I wash my hands. I also wear an apron which I leave in the bathroom while I handle the new bird. But for the first month I try to keep handling to a minimum and just let the bird settle in.
I also keep separate food stock in the quarantine area and any bowls, veggie plates etc... used with the new bird go straight to the dishwasher. I feed a mix of pellets, some seed and a portion of our meals/cooked meals usually twice a day. So for the first 30 days or until the vet gives the clearance the birds spend their time in quarantine. I know this may seem cruel but actually it's far kinder to the bird. It allows them to adjust to this new area quietly and gradually which creates less stress than just throwing them into the mix.
The other thing I do is weigh the new bird twice a day. I would not own a bird without also owning a gram scale (the scale must weigh in grams because ounces are not accurate enough for the small size of birds. Their weight pattern will tell you more than looking at them because all birds hide any of the first signs of illness but their weight will tell on them. I usually recommend Soehnle gram scales.
Anyway best of luck on your new bird and hopefully you and your mom can find a good avian vet to get your new bird a check up from.