One eyelid being heavier than the other is either an eye or a sinus problem. Mine was like that until after my sinus surgery. A tight sticky feeling in the eye could mean either an infection or allergies. The stickiness is either sinus or eye discharge.
Sometimes you can have bad headaches, but most of the time I feel just a vague pressure, and then the weather changes or something, and then BOOM, huge sinus headache.
I'd definately see your doctor, and maybe also an ENT