Does eye booger mean that I am sick or have sinus problems?

Usually not. Most "eye boogers" are simply dried mucus at the nasal eyelid. Sometimes they can arise from conditions like blepharitis or overactive oil glands. They are also seen with allergies and dry eyes. If daily cleansing with warm water doesn't seem to clear them the you should be examined. Sometimes a tear duct infection or chronic eye infection is to blame.