Coming from a parent of a child with many food allergies and intolerances, it sounds like your poor baby is allergic or simply intolerant to his formula. Maybe even to soy, it is a very common allergen. Ask for a referral to an allergist or someone else who can help you diagnose the issues now.
If this doctor doesn't seem to be doing enough to satisfy you, don't be afraid to get a second opinion, or a third and fourth.
And no, they don't always grow out of it. My son doesn't projectile vomit anymore but he still cannot tolerate many foods. More often, the children learn to live with the issues and think the reaction is normal.
You may want to look for a pediatrician or medical doctor that is also a homeopath.
Most importantly, trust your instincts. Mama knows best.