If you are breastfeeding, breastmilk is supposed to help rather than water.
It's probably viral conjunctivitis caused by the cold and will go with a bit of time. It may also spread to the other eye. If it lasts longer than a few days, I'd take her back to the docs who may prescribe eye drops.
When DS has a gunky eye the health visitor and GP advised using a small amount of Johnsons no more tears shampoo in cooled boiled water on a cotton wall pad to clean the eye and that did seems to work pretty well!
Could be the start of conjunctivitis. Usually this follows a bad cold and clears up itself (with the help of a warm compress etc). But if it doesn't, and the eye gets swollen or red, take your dd to the GP as it could be a secondary bacterial infection following on from the viral conjunctivitis.
Hi, this has literally just happened to my 6 month DD. She had sore throat, cough and snotty nose. A day after gunk appeared in her eyes. Doc said if whites of her eyes aren't red it's just snot coming out of the tear ducts. Bathe in cooled boiled water. Lo and behold it was snot as went in a couple of days!
If it's just gunk, then it should go away on its own. But do keep an eye (no pun intended!) on her eye. My dd's swelled to the size of a Ping pong ball and completely closed shut. It was quite scary to look at actually, the whole side of her face became lopsided and swollen. She ended up being two courses of antibacterial drops - the gunk turned from viral conjunctivitis to a secondary bacterial infection.