momof8yrold, my daughter is very similar! Or at least, she was, as a kid. She ate fruits and veggies till she was 3 or 4 and then one day just stopped. We tried every trick in the book, but like your son, she'd throw up. Now looking back I wonder if that's when her IBD started. It is when she was first diagnosed with an autoimmune issue - nail psoriasis. She also always had mild gut issues when she was a kid but we were living in India at the time, and blamed it on food or water.
Like crohnsinct said, we started slow. Realized forcing her was just going to make her hate the food more, so we let her lead the way. One day, out of the blue, she wanted to try broccoli. She liked it! Then it was corn. Then green beans. In the beginning, when she was trying veggies, I made them as tasty as possible - for example, I'd bake broccoli in a white sauce with plenty of cheese and bread crumbs on the top. I did the same with creamed spinach. Over time, we stopped doing things like that and she continued to eat vegetables. I'd say she was 8-9 years old when she started trying veggies by herself.
When she was diagnosed with IBD and was inflamed, veggies caused horrible cramping and diarrhea and we were told no fiber until we had the inflammation under control. Before we were told to avoid vegetables, she had several bad experiences with them, and so she started associating them with pain and diarrhea and cramping.
It took awhile to convince her to start re-trying them but she eventually did. I didn't put pressure on her because during that time she was on supplemental formula which gave her vital nutrients she was missing and knowing how stubborn she is, I knew it would backfire.
Now we do make sure vegetables are well-cooked most of the time - no raw veggies for her except when she has salad. She does not digest everything - we see lettuce in her poop often! We even see baked, home-made french fries in her poop! I'm not sure why since her IBD is under control. But I figure it's better than not eating them at all, even if she isn't digesting everything. We do soups a lot, since she won't drink smoothies. And I do hide veggies in soups - for example, when she was younger and wouldn't eat carrots, I would hide them in tomato soup.
She has just recovered from 6 months of C.Diff. and during that time, she again stopped eating veggies - not altogether, but definitely ate less, due to stomach pain, nausea, diarrhea etc. Now that she is feeling better, we're re-introducing them and she is so THRILLED whenever she gains a food. Never thought she would ever like vegetables based on how picky she was as a kid, but she really does now.
I guess this is a really long way of saying don't give up! Kids surprise you as they grow up.
I do think having his GI talk to him about the importance of fruits and vegetables might help - kids tend to listen to adults who are not mom LOL.