With cry it out you don't literally just leave them to cry. You go back in every few minutes and comfort them so that they know you are still there, but still make them stay in bed. Try it that way plus the routine that others suggested, and it will work

The best thing you can do is just establish a routine. Usually its bath, book or singing, then lights out and sound machine or music. Just have a routine and stick to it.

Sometimes I have to with my son but he’s not actually crying he’s just fussing. He fights his sleep really bad sometimes and will just lay there and fuss, and kick, and violently push his bottle, and paci away. He’ll just fuss and fuss, and fuss, and I’ll be trying every trick that I know bouncing him, rocking him, walking with him, patting his butt, patting his back, rubbing his face, rubbing his legs, and arms, singing to him, talking to him calmly, playing music for him but he’ll just fuss so when I put everything I’ve got into trying to make him as comfortable, and calm as possible, and none of it works i’ll just lay here with him, and let him fuss, and kick me until he finally gives up on fighting his sleep, and calms down, and slowly goes to sleep. I try not to leave him when he’s fighting his sleep (but sometimes I have to, to make him a fresh bottle real quick) because when I leave him he starts crying and it’s the saddest cry in the world I hate hearing that cry from him. I do the fuss it out method because that’s really all my son does he rarely cries the only time he cries is if something scares him or if he poops or if he feels like I’ve left him because when he wakes up from his nap and if he can’t see me then he’ll scream his head off, or if he gets hurt, or if he’s teething really bad

I had my son cry it out, mainly because he was already 1 and a half. The push was that he got his big boy bed because he was big and strong enough to climb out of his crib and I didn't want him to hurt himself.
Just my personal experience of how it went for us at an older age. He never worked himself into a vomit but I would watch him tear his room apart on the monitor. Maybe your lil one is just too little for it right now.
If my son reacted how your describing I think I would've tried it gradually, like instead of fully rocking him to sleep I would've put him down right before he fell asleep for awhile and then put him down while he was rubbing his eyes and yawning a lot and so on.

I know momma's my bf always telling me to do it I just can't we did once and it was horrible , over heard there's different methods to teach them how to self soothe I haven't looked into it myself but I should but I know for sure that there other methods that doesn't require to let them cry it out