Yes, there must be some inflammation for your eyes. When we close the eyes during sleep, the eye nerves will be at rest and the tear glands system will not work. However, you can't help tearing in the morning because the tear gland system works in disorder. You'd better go to see the doctor and have a check on the eyes.
Well, I believe that it is uncommon to see such kind of thing around us. So, It seems that there is something wrong with your eyes now since it is not natural. From my experience, it is neither red eyes, nor infected eyes. But what I recommend to you is consulting a professional eye doctor who could give you professional treatment and advice. It should not be much too serious as long as you pay due attention to your eyes.