We have had the same issue with my little guy only mine is only 9 months old. We went through three months of him beign up all night or making himself throw up. What finally worked for us is this: I follow a strict bedtime routine with him so he knows it is time to wind down. I put him in bed and tell him good night and we love him and I rub his back for a few minutes. Then I leave the room. If he cries, I go in and rub his back or just put my hand on him so he knows I am there. I do not look at him and I do not talk to him. I rub his back until he settles again and leave.
When we first started this, it took an hour or two to get him down without the extreme crying that cases him to get sick. In a few days, it took 30 minutes, then 15 and now, I put him in bed and he usually sings himself to sleep within 10 minutes. This method was recommended by our Pediatrician. She said some children can "cry themselves tired". Others, like my son, cry and they get more and more agitated- not worn out.
Stick with whatever works for you. I know how frustrating it can be. Hang in there!
For what it is worth, I am VERY glad that some of you are NOT my mother. Spanking a child for throwing up? Perhaps I am a bleeding heart. Perhaps it is because my sister in law let my niece "cry it out" even when she threw up and didn't check on her when she stopped. My niece died at 14 months from suffocating in her own vomit because of her mother. Bitter? I sure am. But maybe some of you can learn something from that...