If it makes your eyes sting, or dry, to keep them open for a "normal" amount of time then it seems to me that you might truly have dry eyes. Does it help to use eye drops?
On some levels i can accept the stress issue but ive had it when i was 10 and on holiday in a stress free atmosphere but im happy to keep an open mind and try to find out the cause and find a solution!
It is probably stress. See a neuro-ophthalmologist to rule out an organic cause.
Dr. O.