Hi L., It is true that at around this age, toddlers can develop a bit of a facscination with the gag reflex. My daughter never did it to the point of throwing up -- but she did gag herself a couple of times a day, for about 3 weeks. She seemed to do it most often when she was bored --- I noticed it happened the most in the car.
I looked it up online and saw that many kids do it - often for attention bc parents generally get very concerned when their kids do it.
The advice I took, and it worked, was to generally have little reaction to the gagging. You cant completely ignore it, but dont look too phased by it. When she begins to do it, try to distract her with something. Or if you are right by her, you could show her that she can use her finger to poke at things other than her throat... Like a pillow, or teddy bear, or her tummy, or a book that has the different textures in it (soft, smooth, rough, bumpy, etc).
If she throws up, treat it like it isnt a big deal. Just wipe up, and say "whoops", almost like she just spilled something. It should eventually stop.
I found that my daughter did it the most when I looked very concerned about it.