If you are coughing too hard, IMO you are burning your stuff too quick. Low and slow is the best.
That being said, yes I've puked from smoking weed. It was because this stupid id-git rolled up a bag of seeded no trich crap in a stale blunt wrap and I was trying it just to be nice and hit it, but I puked my guts out. Seeds smell nasty burning. This was the 90's, I don't think I've seen a free seed in 5 years, if you catch my drift. This guy thought that leaving the seeds in made his stuff that much better because he coughs more.
On another note, somehow in the last 2 years I have lost the ability to drink alcohol. One beer, my stomach is upset for hours and I can fight the puking . Two beers, its hard to fight the urge to puke. Three I will be puking before its done.
Shots are insta-puke territory. Yes even the 1oz bar shots.
Don't confuse coughing/lack-of-oxygen for being high.