An allergy test can be as simple as a doctor dipping a small plastic spike in some concentrated allergen, then poking you (lightly, not enough to break the skin, just enough to leave a mark that will fade in a few hours) with both that and a "control" spike, then comparing the redness after a short wait. Pain wise, it is no worse than an ant bite in my experience, and I was tested for the 50 most common allergies at once (we were trying to ID the source of some symptoms I was having).

IANAD though, so testing for celiac disease may require more.