i can understand how painful the situation would be if the children are ill..
need to know few more things....is he putting on weight,does he weigh double his birth wt now,,is the child active,does he have fever
,,does he receive vaccinations as per schedule...
any blood tests,x ray
,crp etc...taking any antibiotics
i dont think the problem is with milk...but he may need healthy diet supplements along with milk(to boost up his immunity levels),care during feed to avoid aspiration,personal hygiene and clean home and surroundings....avoid child to expose to smoke,dust,plant pollen, grass,pets...
do not worry....child will be absolutely fine
bye take care