My only suggestions other than eye drops (why no eye drops? Anyway...) are to vape or be careful about blowing the smoke out a window or generally away from you. (As I'm aware, you get red eyes from a number of different factors, and getting the smoke in your eyes is definitely one of the bigger factors.) Typically, I notice my own eyes only get red if I'm sitting in a powwow with my friends and we don't blow the smoke away and instead allow it to linger among us.

Looking online, I've seen suggestions to drink water beforehand as well, though whether that works is not something I know.