Here is a video that shows pus being remove without cutting. Note that this person is saying that the pus is from eyeworms, but I do not think your hen has eye worms, I think your has a full-blown sinus infection from some sort of respiratory disease.
Warning - graphic
Warning - graphic
So I will have to press real hard like if I was popping a pimple it seems like. After I remove the pus from the pullet’s eye what should I do? Should I put her back into the isolation stall?