My baby's eye

So my daughter is getting rid of a cold. Her eye at one point she couldn't open due to tearing and it drying up while she was napping. Sometimes I see green puss coming from the eye. The doctor said he didn't see nothing wrong with the eye and the tear duct is probably clogged. I was told to continue the warm compressions with a wash cloth but it's been over a week now and it hasn't gone away. She constantly has her hands in her mouth and rubbing her face. Should I get eye drops? Would saline solution (contact solution) help disinfect her eye? Would it hurt her eye? At times her eye looks better but then she goes to sleep and wakes up and it's the same. The red lines in one eye are more than in the other which I think would mean it's irritated. Any suggestions??