My baby all of a sudden was projectile vomiting last night.

And then I gave him a formula bottle in the middle of the night and he throw that back up. I gave him some water and he went back to sleep.

This morning he had a bit of cherrios and water with sugar in it , but now has the runny poops but hasn't thrown up,

Call your Pediatrician and ask - no one can possibly diagnose this without seeing the baby and, even if we could, it would be dangerous to guess.

Projectile vomiting can be caused by a serious condition called pylorea stinosis
So you need to contact your pediatritian asap. It might be something simple like acid reflux but better safe than sorry. I went through something very similar. Don't take chances. I hope everything works out that poor baby

My baby all of a sudden was projectile vomiting last night.

And then i gave him a formula bottle in the middle of the night and he throw that back up. I gave him some water and he went back to sleep.

This morning he had a bit of cherrios and water with sugar in it , but now has the runny poops but hasnt thrown up,

Since he has had some vomiting, and now loose stools, it sounds like it might be a viral or bacterial infection, or stomach bug. Often they just have to run their course, but obviously you will keep an eye on how he is doing.

As was said, best to have him seen if it continues. Also, it's a good idea to avoid adding sugar to his water. If he is no longer vomiting, continue with his usual feeding schedule. If you give him water, small amounts of plain water would be preferred. Although it usually is used when there is more elimination occurring, his doctor may suggest small of amounts of Pedialyte.

Keep an eye on him... hope he feels better soon!