According to your description, the red eyes are not caused by headache. It is possible caused by lacking of good sleep. Or you just stay up to late last night that cause the red eyes. If so, take a good rest, your eyes will be clean from red eyes. If you also feel itchy and burning eyes, then, things may different because it may caused by allergy eye infection or pink eyes. If this happy, getting rest can't reduce the redness in the eyes. You shall treat your eyes with antibiotic eye drops.