It doesn't really sound like allergy to me, but then I'm not an expert.
It would seem, from what you tell, that the most common type of allergy to super glue is a skin allergy and what you're describing sounds more like the type you get from pollen and dust.
I would simply put it down to a simple reaction of the mucus glands in your nose. The glue will probably dry out your sinuses, and that can result in some overproduction of liquid. This can also make you react to other things such as pollen.
As for the itchy eyes I get that too if I get to close to the stuff. I think it does that to everyone.
Use plastic cement for plastics and open a window when you use the super glue to get some airflow. Also you should probably, and that goes for all solvents, try to limit your exposure to them. 12 hours is a really long time to be sniffing glue.
I don't think there's any reason to panic, just think about what you're doing and the amount of time you spend with the glue. If you don't feel any improvement you should of course go see a doctor.
Also it would seem that alot of my english vocabulary is related to nasal fluids.