I took a look at your earlier conversation on Facebook to get some background. I also have a high school senior with chronic migraine. It is more difficult to deal with your child having migraines than it is to face them yourself.
To start with, if her doctor isn't responsive or helpful, then it's time to fire him and get a true headache specialist. No one should be facing 4 weeks of migraine attacks without aggressive and responsive treatment from the doctor. Frankly, I'm surprised your doctor hasn't recommended an inpatient hospital stay with IV infusions to get the pain under control.
How long has she been on Zonisamide? Is this her first preventive? It can take up to 90 days to see results from a preventive medicine. I take a couple of preventives and sometimes I do miss a dose here and there. The only time I have experienced a flare up of attacks after missing a dose was when I went several days without the medicine. Otherwise, an occasional miss hasn't created a problem for me. I'd be looking at weather changes, missing meals, sleep problems, dehydration, or something in her diet as a potential trigger.
I'd also be pushing back on the doctor for a differential diagnosis to make sure she actually has migraine and not some other headache disorder (i.e. Occipital Neuralgia or Hemicrania Continua come to mind).
As for the triptans...keep trying. With long lasting attacks, she may need a longer-lasting triptan (Frova or Amerge are good choices). They take longer to kick in, but stay active for days to keep the attacks at bay. My son doesn't have very good luck with triptans alone. Instead, his specialist has him take 2 naproxen and 1 Zofran along with his triptan. That seems to help a lot.
If her pain is bad and non-stop for more than 72 hours, she is at risk for Status Migrainosus and should be checked out by a doctor to rule out serious complications. If her doctor won't see her, then go to the ER and explain what is going on. They should do a neurological exam to assess for serious problems. Once it is confirmed that she is only dealing with a refractory migraine (most likely), they should give her IV meds to get the pain under control. Most often it's a strong NSAID, something for nausea, and occasionally solumedrol or magnesium. Every ER and every doctor is different, but most ERs have a standard protocol for migraine.
If she's waking up with attacks, please ask the doctor about getting her tested for any sleep disorders. Often, an undiagnosed sleep disorder triggers morning attack and makes it nearly impossible to get relief from preventives. A good headache specialist will want to rule this out.
Here are some links to information you might find helpful:
https://migraine.com/blog/looking-for-a-migraine-specialist/
https://migraine.com/blog/is-it-time-for-a-new-migraine-doctor/
https://migraine.com/blog/when-doctor-er-for-migraine/
https://migraine.com/living-with-migraine/migraine-and-sleep-disorders/
Please write back and let me know how she is doing. I know it's nearly impossible, but do try not to worry. But don't be afraid to be a "momma bear" on her behalf if you need to. I also keep an eye on the Facebook page, so reach out to me either way and I'll respond.
Tammy