Hi Trincity! I met you on another thread you started. I hope all the chicks are doing well and have some space to romp.
This chick isn't trying to vomit. It has something going on in its crop. It may be impacted. Have you been feeding grit to your chicks? If you've been feeding them scratch grain or something other than chick crumbles, they need grit. You can buy it at a feed store or go outside and dig up a clump of soil from your yard. Keep the grass on it. Give it to the chicks in the brooders and let them eat the dirt and nibble on the grass. It will act as grit so they can digest their food better.
Back to the sick chick. Try holding a small saucer of olive or coconut oil or mineral oil under its beak and see if it will suck some up. There's a good chance it will. If it refuses, try dribbling a little bit of oil at a time into the right side of its beak with an eye dropper. Careful not to force it down its throat or it could aspirate the oil down its wind pipe.
Next, try massaging very gently its crop in a circular and downward motion. That will help to break up the mass in the crop and help it to go down. Offer the chick some fresh water after you're done.
It should start feeling a lot better right away.