Yes, she could even make some breathing noises even if she had something in her throat when she was picked up. Most of my hens absolutely freak out when I pick them up.
Eye infections or conjunctivitis are usually caused by injury, stings, or by respiratory infections. If you aren't seeing sneezing, runny nose, and rattly or wheezy breathing, then it may be an injury. Removing any pus with QTips and tweezers will help get the eye cleaned out. Saline, Vetericyn...