Hello, first you should know that no one's eyes are perfectly the same sizes. Mostly, one eye will be a little bigger or smaller than the other. Few people finger out this just because they are not as careful as you. And yours may be more noticable. But, in some situations, it may caused by some eye problems and thus it could be a serious problem. So, you'd better go to the hospital and have a check, then things will be clear.
I am not sure. Eyes stick out can be related to a serious problem like thyroid disease, eye lid problems or tumor in the socket. And according to your description, i can't judge what causes one of your eyes sticks out. So, you'd better visit an MD ophthalmologist right now and get your eyes checked. I hope you fine. Good luck.
It is not normal. Your eyes infection or the coming invisible bacterium in your eyes may cause such symptom. You'd better use some eye drops with anti-inflammation to release the symptom. You could also put the clean cloth to soap into the hot water and then squeeze it. Then you put the warm cloth on the surface of the eyes. Your eyes will feel comfortable.