It definitely could be anxiety. The mind is a powerful part of the body and can induce physical symptoms.
I have MH issues myself and if I'm very distressed I get really horrific diarrhoea. Anxiety can also cause for me strong palpitations, nausea, dizziness, fainting (which I'm prone to anyway as I have POTS and a natural tendency to VERY low blood pressure).
Is the anti sickness medication he's been given the same as he's tried before? And even if so the same dose?
Because different meds work for different people and sometimes a simple change like a higher dose can help too.
He could also consider home/natural remedies in addition to the medication (providing the med info leaflet doesn't say contraindicated)
Things like:
Herbal teas (ginger and peppermint are the obvious ones but if anxiety is a possible cause there are some that can help with anxiety too - peppermint is supposed to help with that too, as is chamomile, rose, lavendar)
Aromatherapy
Self massage (many of us do this instinctively to self soothe)
Regular but "peaceful" exercise, the obvious one that will spring to people's minds is yoga (which is a damn sight harder than it looks!) but also simple things like walking, swimming
Having a good sleep schedule (I massively struggle with this but might help him)
Cut out caffeine - I've done this and I've really noticed an improvement
Cut out alcohol - people tend to think of it as a sedative/relaxant but it's actually a stimulant too and can cause anxiety symptoms. Family/friends have discovered kind of by default that for them certain drinks make them anxious and others don't
Cut out smoking - again a stimulant but can also affect the stomach, many don't realise.
Some "normal" foods and drink can increase/reduce anxiety too.
Calming foods are those that contain omega 3 & 6, vitamin d, iron, selenium, tryptophan. Mainly dairy (sorry he's allergic isn't he?) nuts& seeds and oily fish - how's his diet?
Also even from a purely physical point of view certain foods can cause nausea
For me there are a few that do that, some spicy food, citrus fruits, some berries, certain nuts.
Might be useful to keep a food diary, he may have developed another food allergy?
Regarding his dad's comments though is it possible something in the environment of the place he's going to is triggering nausea?
I have asthma but it doesn't always present as wheezing/breathlessness but certain airborn/aerosolised things can trigger a nausea based reaction.