Sounds like her tear ducts are blocked. It's very common but often clears by 12 weeks and generally is in one eye.

Both my girls have had it and DD2 (9 months) still has it so we are going back to the Opthomologist this week to book in the surgery. As much as the surgery is a little nerve racking (although they assure me it's super quick and simple), I'll be SO glad to see the gunk gone for ever. It's driving both her and I batty and with all the rubbing she's at risk of scarring.

I'd see your GP and get a referral to a specialists.

PS: if it's severe enough, they will definitely do the surgery earlier. They were going to do DD's at 7 months but her actual eye was still fine so he suggested we hold off unless the rubbing and redness increased, which it has.

Also, don't use tissues if you can avoid it. Small fibers can rub off into their eyes. Get the Little Eyes wipes from a pharmacy or use a very soft, damp face washer.

It's horrible, I feel your pain