It sounds like your leo has an eye infection. If it were me, I would be taking her to the vet as soon as possible. The vet will be able to clean out her eye a bit and give you antibiotics or other meds for her.
To get the eye to open you can use a warm moist paper towel applied to the eye as you hold the leo, and after it softens they can usually get it to open. A vet check for an infection seems like a good idea also.
I wouldn't advise using certain q-tips around animals eyes. Q-tips can leave behind bits of cotton which could lead to further complications for your leo. You never know if a q-tips tip is going to be a little lose, then woops.
That is one of the reasons along with damaging walls, is why its not advised to use q-tips inside peoples ears either.