My son had this.
My doctor said that the term for it was "gummy eye" LOL
It cleared up by the time he was 6 months, we just used saline on cotton pad thingies to clean it. It was worse when he had a bit of a snotty nose. (could always tell he was a bit "off" cause it would be worse KWIM?)
I also had the same thing and at 6 wks of age, the doc took me off mum and went into another room with a nurse and "fixed it". Mum said the noise I made was horrific
So I am glad it is done differntly now.