It looks like your kid is having gastroenteritis
Have you taken him to your doctor? If not please have him seen as its already 2 weeks now.
For repeated vomiting, he will need medicines like Domperidone
Since he has both loose stools and vomiting, his hydration has to be taken care of. Give him plenty of fluids avoiding milk and fruit juices. You may give him vegetable soups, plain water, curd, ORS.
Boiled potato, Rice based porridge will be good.
sachets (Econorm, Bifilac) can be given that will reduce the frequency and duration of diarrhea
Since its 2 weeks now, its better to have his stool examined for reducing substances, ova and cyst.
Mostly below 2 years its viral. And after such an infection, kids may develop temporary lactose intolerance
. In such a case you might have to stop his milk for some time.
Hope my answer helps you.
Wish a speedy recovery for your kid.