Are swollen eyelids related to the cold/flu or nasal cavity infections? or menstrual cycles? 24+ hours of swollen non-itchy non-red eyelid, what do?

It would require: an evaluation if you have symptoms that might be suggestive for each of these conditions.

Swollen eyelids: Do your eyelids swell every time you menstruate? if not then why would you think they are related this time? You clearly indicate a history of environmental allergies which could certainly cause swollen eyelids; however, since there are no pictures to evaluate extent of your condition, I would recommend you see your doctor if swelling persists despite OTC antihistamine use or change in vision.