I never heard that pink eyes can cause stuffy nose. Pink eyes is also known as conjunctivitis. And allergies, bacterial infection can sue pink eyes. And people who suffered from pink eyes will suffer redness in the eyes, puffy eyelid, eye pain as well as itchy eyes etc. But pink eyes have no connection with nose. And usually, stuffy nose are caused by cold and hay fever etc. So, You shall treat it in a right way. If you don't know what causes it, just consult a doctor for a right treatment.
Well, I don' t think that pink eye can cause your stuffy nose. How can you know what you get is pink eye? Usually, pink eye will not arise stuffy nose. Maybe you are just thinking too much, maybe what you get is very common red eyes. Don' t scare yourself. Let me guess, maybe you just get a common cold, and then your eyes get irritated by the bacteria. By the way, if what you get is just common red eyes, you will recover soon. On the contrary, pink eye will drag you for days.