Hi Nick. I'm afraid I can't advise as to the asthma side of things; but surely finding a less exposed place to run would benefit you for starters? (can you
get more exposed than the Humber Bridge?).

Luckily for me, I've never had to contend with the same problems that you have to, but in strong winds I too find breathing efficiently can be a problem, and wherever possible I'll try and choose a more sheltered running route.
Good luck.