Why would you NOT let her have the nitrous, is it too expensive? It may be the only thing that keeps her from running out of the office, and if you've ever had teeth pulled, it sounds like someone is inside your skull with a pair of pliers crushing bone, which sort of is what they're doing, breaking bone and tearing flesh and nerves to get the tooth out.
If the cost of the gas is inflated too much, you could see if they can give her a xanax to take before going in, but that wouldn't help nearly as much during the procedure. Even if they get the novocaine in just the right place to numb the nerves, it may not be enough to stop the pain, so the gas would take care of the mental side of that, and some of the physical. Mainly it just makes it so that the panic is farther away and doesn't seem as important.
For a while they wanted to pull four of mine when I had braces, but for whatever reason my parents decided against it, which was the right decision. Later, at 15 or 16 I did have all four unerupted wisdom teeth extracted with just nitrous and novocaine. Some people do it under general anesthesia, which tells you how serious it is. It's possible that it's not too late for her to get enough fat soluble vitamins (D, K, A, E) to allow her jaws to grow some more.
But if it genuinely has to be done, you can tell her to just think past the procedure when it's all done, and to have an attitude of just getting it out of the way so she can go back to normal; that it'll hurt for a while, but not terribly and not more than she can stand. You just try not to move your jaws for about a week til the swelling goes down, and have a spit bucket for blood for the first day or two. I wouldn't think she'd need to miss more than a day or two of school, but it depends on how bad it hurts.
y: It's pretty ignorant to say she's freaking out over nothing or that having teeth pulled is no worse than getting a shot.