Cows milk allergy??

Hi all

Really don’t know what’s going on with baby. He is 3 weeks old and on formula. He is constantly throwing up half of his feed each time he feeds. He is so gassy all of the time.

When he has his feed his stomach immediately starts bubbling and he looks uncomfortable.

He also had this type of poo in his nappy every single nappy change.

I’ve also noticed his breathing is quite fast and funny which we was in hospital in last week but they discharged him thinking it was a chest infection.

Any advice??

Thank you