Is this a migraine ?

My son (14) has been having severe headaches each morning and vomiting that slowly gets better during the day. This has been going on for 6 days. We have had two hospital visits with no diagnosis or treatment apart from fluids and paracetamol/ibuprofen. His pain level is a 9 in the mornings. Falls asleep for a few hours from 10 am and then after around 3pm he is back to “normal” with a head pain level of 3/4 rather than 9/10. Can a migraine go on this long and does it sound like a migraine - has anyone had any similar experiences?