Can you catch the cold bug through your eyes?

Asked by tan253 (2948) November 28th, 2016 from iPhone

My daughter is quite sick. 39 degree fever, she’s well looked after!
She had her hands in her mouth and went to hug me but she stuck her finger straight in my eye! I’ve been doing so well so far to not get her flu – has my luck just run out? Saliva from mouth to eye? I rinsed my eye with water but I fear it may be too late. Thoughts?