The starting point for treating simple hayfever is antihistamines, yes, but some people have 'hayfever' that's technically seasonal asthma triggered by pollen - the cough, tight chest and wheeze the OP describes sounds like this is the case. These people get prescribed inhalers just like people who have asthma all the year round ... it's not the doctor making a mistake.
OP, I'd make an appointment with the doctor (you're not wasting their time - they need to check the inhalers are still appropriate/sufficient, that's why repeat prescriptions don't run indefinitely). Do the doctors know you're getting symptoms/needing to use the inhaler most of the year? If they don't know, or you're using it more than twice a week, then ask for an urgent appointment as you need to be re-examined.