Its been 4 months he is going to the school... And he use to vomit every single day... Except when he is at home he does not vomit...
This is not very good. He may be stressed due to unknown faces, perhaps there is pressure to do things he doesn't like, he has bullies in his section, his teacher may be shouting at him (of course, won't admit).
You have to talk to your son, ask why. Keep asking with love and care. Keep an option of not going to that school but some other teacher... You have to keep the possibility of changing school in table.