As far as I know, stress won't cause swelling eyes. Swelling eyes are usually caused by allergies, conjunctivitis (some people also called it pink eyes). Besides, styes, chalazion, eye injuries, contact lenses wearing or blepharitis can also make eyelids swell. If you want to cure it, you shall know what causes it. Anyway, you can apply cold compress which can help you reduce the puffiness of the eyes.
I don' t see that happen. I know several factors which can lead to your eyelids to swell, including conjunctivitis, allergies, a sty and so on. By the way, it also happens to pregnant women as well. And as you may know, conjunctivitis is also pink eye. Once you get pink eye, your eyelids can get swollen quite fast and easily. However, according to your description, your swollen eyelids may be caused by allergies. Try to see if you can relieve this yourself. If you can' t, you can only go to ask a doctor for help. I suggest you not to take any measures before you see a doctor.