Except the article states that those aren't useful. (Maybe you are trying to tell me the article is wrong?)
> One problem with wheat allergy is that there is no good test for it. In fact, the blood tests for IgE (called RAST tests) are notoriously unreliable; for example, only one in eight children with a positive IgE test for peanuts is truly allergic.
> There’s not even a mediocre blood test for gluten intolerance. The diagnosis simply relies on someone’s subjective feelings of bloating, bowel changes, or mental fogginess after eating gluten
Well, as far as a test for allergies with intestinal symptoms, you could get an endoscopy/colonoscopy and possibly a biopsy while they're at it. A gastroenterologist should be able to tell you more.
So I've spent hours today looking into all this stuff. (This may be TMI for you, but I leave it here in case it helps someone else.)
I actually had a biopsy, but they took all their samples from above the duodenum, not in/below it. For gastroenteritis (stomach inflammation)/vomiting, it makes sense to take them above the duodenum. To make a ruling for coeliac (where it seems that food does not come back up, but apparently is more likely to go out the other end?), you have to take them in the duodenum.
The results of my biopsy were positive for gastroenteritis, which just means you have stomach inflammation, but doesn't tell you anything about what's causing it. They thought it was from coffee/soda, but I now know that's not right, from personal experience with glutinous foods.
[1] - https://en.wikipedia.org/wiki/Allergy_test