It sounds like it is not coincidence but eye infections are contagious if you are in the close contact with the infected person or if you are sharing the same cosmetics. Symptoms you have described resemble bacterial conjunctivitis. This is one of the most annoying eye infections ever!
I had it few times in my life and I absolutely hate it. When I notice that my eye is red, inflamed and watery I am ready to cry in that very same moment, and I am a guy. And this thing is very contagious so you must be careful all the time and wash your hands and have only your towel and cosmetics.
Have you visited your doctor or you are waiting for infection to pass by itself? I think that the only way to find out was this a coincidence or not is to find out what is the name of the infection that your friend has and afterwards what is the name of yours.