I never had a problem with contacts, but I have a friend who has been trying to use them for the first time this year. He hasn't thrown up, but he does get sweaty and lightheaded. Poor dude, it is ticking him off because he figures a 40 year old grown man should be able to do it.
It sounds like your son is on the unhappily normal side. :-( He can either try again, or stick with his glasses. Whichever choice feels right for now.
My kids have both worn glasses since age 8. My younger son was resistant to getting glasses at first, but not wearing them isn't an option; there would be consequences. Not wearing the glasses is not a choice that I allow my kids to make.
What they DO get to choose is their eyeglasses style. If your son's current glasses are uncomfortable or he doesn't like the look, that is something you can change.
Check out zennioptical.com, it's a great deal and quality work. Everyone in my family has had glasses from there at some point. My husband's current glasses cost under $17, including shipping.
Re: Doris Day's age comment - Back when I was young, contacts were either rigid and difficult, or softer lenses were worn for a year at a time and required multi-step and multi-product care. Back then, an older age for starting contacts was in order.
Now that contacts are usually replaced every day or week, the risk of infection is much lower and the care is one-step and super easy. The average age range for children getting contact lenses is 8 to 11 years old. Kids in this age group have a 90% success rate of appropriate self-care and use without parental help.