It could be a combination of hay fever and something else.
Back in my teaching days, I would hardly notice my hay fever most of the time but it sensitised my eyes and nose to some things which wouldn't bother me at other times of the year. For example, I had to minimise my use of the blackboard as far as possible because the smallest amount of chalk dust would produce hay fever symptoms.
Similarly (and possibly importantly here) walking into a room with a humid atmosphere would start my eyes and nose itching and streaming.
So, based upon my own experiences, I suspect that you might have hay fever which is unnoticeable most of the time but 'set off' by a humid atmosphere.
Try taking loratadine tablets. A month's supply only costs a couple of quid in Asda:
https://groceries.asda.com/product/allergy-hayfever/asda-oneaday-hayfever-allergy-10mg-tablets-loratadine-tablets-30-pack/910001308087