The exact same thing happened to me when i was 16, I've dealt with constipation my whole life but it got really bad and eventually i started throwing up and lost my appetite for 2 weeks. I don't think you can be so constipated you vomit in the way that you're thinking; i think when you're constipated the muscle and nerve spasms in your intestines get all messed up and confused and want to eject food because there's too much food, then more food comes in and its a reflex panic reaction that happens. If your daughter thinks she might get constipated because her colon's nerves don't function smoothly (espc. if this happens more often under stress or at a certain time of the month) then i think it could be a nerve/muscular problem like (i think) i have...
This is not based on any medical knowledge i have(just experience with IBD). It's just an assumption. Find the right doctor. If your doctor doesn't have the solution you need, you're allowed to find another one. Trust me there are very few really good ones.
hope i gave you something --Lena