Your son has multiple allergies and by 'immunising'' him, the Allergist probably meant starting immunotherapy
This is reserved for those who have failed optimal medical therapy and currently not licensed for his age at least in most centres in Europe (pending completion of trials).
If he has asthma, he will need optimal management for that to prevent a worsening of the allergies.
leads to asthma in the long run, so you must remember that.
His medical treatment for now should include: cetirizine
syrup 5ml twice daily, olopatadine
eye drops, nasonex nasal spray
1 spray / nostril once daily with addition of montelukast
4mg at night if required. This should be continued for 6 months and definitely during winter/summer months.
Only if he fails this and reaches age at least 8-9 years, immunotherapy should be considered.