I'm the one Bog was saying has a dd who dealt with VCD last year. My dd had an extreme case, so please don't let our experience scare you! It was hell for us, but, as I said, dd's case was not the norm. She had VCD every single waking moment for 10 weeks straight. As a 11/12 year old level 9, her gymnastics season stopped, and her life was altered. She was completely out of the gym that whole time and even for about a month after as she recovered physically and mentally from the exhaustion of struggling to breathe, being physically inactive (which is actually tiring), and being poked and prodded everywhere (including her mind.) Instead of doing many of her normal activities, she was shuffled to a large number of different types of doctors and health care providers for second and third and fourth and fifth opinions: ENTs, speech therapists, sports psychologists, another psychologist, our regular doctor, an alternative counselor, etc. No one could find a real reason why this was happening; nor could they find a solution, other than a couple breathing techniques to sort of quiet her breathing a bit. She still constantly worked hard just to breathe. (We called her Darth Vaderess to try to lighten it sometimes, but she did sound like a little Vader.) Yes, my dd obviously had the super-achiever personality and history associated with VCD, but no one could find any evidence of stress or anything in her that would cause this. She was even hypnotized twice. In the end, it was a kinesiologist/chiropractor who discovered that she had high levels of mercury and arsenic in her system. That professional said it would take a certain number of weeks before it completely left her system, and she was correct to the day. (My dd did not know the number of weeks, btw.) When one has toxins in the body, candida builds up and causes the vocal chords to slam shut at the top which is, as you know, what VCD is.
The good news for us is that my dd did recover, and she hasn't experienced VCD since (knock on wood; oh, please, God!). Once she recovered mentally and physically, she went back to gym, and she's quite happy. Plus, she's discovered that she is amazingly strong mentally, and she has remarkable faith.
My advice? Make sure the ENTs and speech therapists have had a lot of experience with VCD. (It was so frustrating to go to a couple appointments with people who claimed to have vast experience only to discover they really only had worked with a couple or a few people with it before, and none with severe cases like my dd's.) It's a condition of which little is known, actually, so even those who deal with it may be a bit clueless or helpless. Seek out as much help as you can from different areas, and don't be afraid to go to a couple kinesiologists to see if something might be going on with toxins like what happened with my dd. Try to find the best in each field. Keep in mind that you parents are your child's strongest advocates, and you know her best.
Also, it's helpful to have your dd start a positive, healing journal if she doesn't have one already. My dd, husband, or I would find meaningful quotes, verses, or songs, read them together, and she'd pick ones to write in her positive, healing journal. She still puts entries in it pretty often. Plus, even though dd's wasn't caused by psychological pressure, we meditated, and I stayed next to her side every night as she fell asleep, helping her to relax so she could rest. It doesn't sound like you need to lie next to your dd as she falls asleep, but the practice of meditation will likely help her mind and body (including the VCs) learn to relax on demand (hopefully).
You already know, I'm sure, that the breathing techniques that will be taught to your dd by the speech therapists might be able to help her stop future attacks. That's excellent, obviously, as it's quite a panicky feeling to not be able to control your breathing. Deep relaxation, as I mentioned, is also key. (Inhalers, however, do not help VCD, as, like you indicated, they help the chest, not the vocal chords, open. Inhalers would help exercise-induced asthma, though.) Especially if those techniques do not work, however, look for deeper issues.
I hope I didn't frighten you. I'm sure your dd's VCD will fall into more of the normal type that comes and goes very briefly and can be stopped by relaxation and breathing techniques. It's still worth investigating thoroughly, though.
Good luck! If you ever want to "talk", feel free to pm me.