What does her Pediatrician think? sorry, that is the Hospital your child goes to?
Most states, have an Early intervention program, which is "free" through 3 years old. In my state it is the zero-to-three program. Try asking your Pediatrician.
It is a program, for including speech therapy, whereby they do an overall developmental assessment of your child. If your child has speech "delays" or just needs help, then they come to your home.
My son had that from about 19 months old. He was late in talking...but in My son's overall development, per his assessment, he was found to be above par and even advanced in many areas. Just his talking... was later. Though there was not anything "clinically" anything wrong with him. He just needed encouragement and help with forming his words. Things that only a speech therapist can give you tips about and/or debunk anything that a lay-person may or may not know.
For example: at EACH age juncture, developmentally, saying certain words are not yet developed, ability wise. There are "front of the mouth" sounds, and "back of the mouth" sounds, and words that combine throat AND tongue/mouth coordination etc. So naturally, she will NOT be able to say certain words, yet. Keep it all age appropriate.
My son really loved it as did I. He is now the most talkative one in our family.
Sure, each child is different. And they talk when they are ready. And talking "late" has NOTHING to do with intelligence. Einstein... didn't talk until 3 years old.
I don't know why they have to sedate her for a hearing test. MOST Pediatricians can do that... have you asked your Doctor? THEY don't sedate the child for it.... they can observe hearing in other ways.
I would, go through your Pediatricians advice and assessment. My son did NOT have to have a hearing test... at all, to have services. AND, as a Mom I was able to call them (the intervention program) directly, and request an evaluation. I did NOT have to go through the Pediatrician... although I informed them of it, so that they could note it down in my son's chart.
You can also try and teach her sign language.... so that she can convey to you her thoughts. Teach her "functional" words: hungry, milk, sleepy, mad, happy, etc. My son knew sign language and the Speech Therapist also says it is good. It supplements their communication. Then they will grow out of it as they speak more... and can communicate.
All the best,
Susan