My 1 month old baby is being fed with hidrolized milk cause dr suspects shes intolerant to milk protein. will she grow up normally with this milk?

Yes: If she is indeed milk intolerant, these hydrolyzed formulas have similar components to regular formulas. Their protein source has just been partially broken down to avoid the bodies reaction to whole proteins. As she gets older her needs or true intolerances may become clear at a point where her size has increased to the point alternative feeds is not as risky.