Hi - I've Had A Cold For Five Days Now

Hi - I've had a cold for five days now with lots of coughing, sneezing, runny nose, headache, and sore throat off and on. Today my right eye seems to have become involved with a lot of gunk, it weeps continually, and the eyelids keep getting stuck together. Never have had this happen before. Is it a sign of sinus infection? (Don't think I've had too many of those so new thing to me). Will be flying to California next Wednesday and would like to get this all cleared up before I go, if possible. Should I see a doctor and get on antibiotics if I do have a sinus infection. Thanks for your help!