Suggest Treatment For Vomiting In Children
He should be seen by a doctor.
Detailed Answer:
Hello and welcome,
There are a variety of causes for vomiting in children your son's age, but as it has been going on for over a week, it is time for him to be seen by his family practice doctor or pediatrician.
The most common cause for vomiting is gastroenteritis (stomach "flu"), which in the US is usually caused by a virus. This will resolve on it's own, but is usually gone within a few days.
Anxiety can cause vomiting too, but not usually with every meal.
More concerning causes include appendicitis (usually accompanied by right lower abdominal pain and nausea and sometimes fever).
I am concerned that he is always hungry now. This is either because he is not keeping enough down, or he may possibly have a blood sugar problem which can have symptoms of needing to eat a lot, drink a lot, and urinate a lot.
So take him in for an exam. It would also be good to get a urine specimen (which can show abnormal presence of sugar and protein if a sugar problem), and a blood test (Complete Blood Count with differential, Blood Sugar).
I hope this helps. And that he is feeling better soon.