My DS is doing GCSEs this year and always gets terrible hayfever in exam season. The routine we tested last year and trying again this year is:
Fexofenadine (currently 120mg which is the most the GP would prescribe for hayfever)
Beconase for children nasal spray - Nasobec aqueous seems to be the same, both are steroid nasal sprays, for children they have to be prescribed as the OTC ones are a different strength for adults
Sterimar hayfever and allergy relief nasal spray - recommended by a friend whose child has multiple allergies. It's basically a saline nasal spray with fancy additions but it does seem to work more than the cheaper "standard" saline sprays, DS tried a few sprays and prefers Sterimar. He uses it in between the beconase doses
Haymax ointment around nostrils and under the eyes - again recommended by my friend - it's not the cheapest so I am sure vaseline would also be ok
I wanted him to use eye drops as well - sodium cromoglycate (Opticrom or similar) but he refuses to put anything in his eyes, unfortunately.
If the above fail I am going to suggest he takes a different antihistamine as well as the fexofenadine. Maybe clarityn as others have already said.
The other thing re: exams is that if he has exams on a day when hayfever badly affects his performance he can ask for "special consideration" from the exam board, it allows for a small uplift in mark due to acute conditions such as hayfever. It's obviously counted as a minor factor so it's only a possible 1% uplift but it could be the difference between a pass and fail. So I"very reminded my DS to bear it in mind and speak to the invigilator after the exam if his hayfever is very bad. That hasn't happened at the moment though.
Unfortunately we have to dry washing outside as we have no dryer, but my area doesn't have grassy back gardens so hopefully pollen isn't going to be too bad on the clothes.