This is what NICE has to say:
"1.5.10 For people under 16 who have sustained a head injury, do a CT head scan within 1 hour of any of these risk factors being identified:
suspicion of non-accidental injury
post-traumatic seizure
on initial emergency department assessment, a GCS score of less than 14 or, for babies under 1 year, a GCS score (paediatric) of less than 15
at 2 hours after the injury, a GCS score of less than 15
suspected open or depressed skull fracture, or tense fontanelle
any sign of basal skull fracture (haemotympanum, 'panda' eyes, cerebrospinal fluid leakage from the ear or nose, Battle's sign)
focal neurological deficit
for babies under 1 year, a bruise, swelling or laceration of more than 5 cm on the head. [2023]
1.5.11 For people under 16 who have sustained a head injury and have more than 1 of these risk factors, do a CT head scan within 1 hour of the risk factors being identified:
loss of consciousness lasting more than 5 minutes (witnessed)
abnormal drowsiness
3 or more discrete episodes of vomiting
dangerous mechanism of injury (high-speed road traffic accident as a pedestrian, cyclist or vehicle occupant, fall from a height of more than 3 m, high-speed injury from a projectile or other object)
amnesia (anterograde or retrograde) lasting more than 5 minutes (it will not be possible to assess amnesia in children who are preverbal and is unlikely to be possible in children under 5)
any current bleeding or clotting disorder. [2023]
1.5.12 Observe people under 16 who have sustained a head injury but have only 1 of the risk factors in recommendation 1.5.11 for a minimum of 4 hours from the time of injury. If, during observation, any of the following risk factors are identified, do a CT head scan within 1 hour:
a GCS score of less than 15
further vomiting
a further episode of abnormal drowsiness.
If none of these risk factors occur during observation, use clinical judgement to determine whether a longer period of observation is needed. [2023]"
I would say he meets 3 X discrete episodes of vomiting followed by further vomiting = head CT. Hopefully he is absolutely fine but I think he does need further assessment in ED to consider a head CT. I would skip 111 as they will rightly instruct you to attend ED. Just go straight there.
(Genuinely do see lots of kids with head injuries and coincidental tummy bugs. However, best to have a cautious evidence based approach. I always think "what would I want for my child?")
Good luck x