Why does my eye lid hurt when I blink. 23yo female suffering a cold?

Stye or pink eye. It is not uncommon to get conjunctivitis, or "pink eye", when you have a cold, as they are often caused by the same virus. If your eye is red and you have discharge, that is likely the problem. You may also have a hordeolum, or "stye" under the lid. Hot compresses are helpful for a stye. Sometimes antibiotic drops are helpful for either of these conditions.
See below. The possible causes of this symptom are: a foreign body in your eye, a stye, the beginning of an eye infection, insect bite or trauma to eye, among other causes. Please see your doctor to have your eye examined to make the proper diagnosis and possible treatment.
Congestied sinuses. Could be sinus congestion because of your cold. Try taking decongestant.