As discussed, I suspect that your pet may have developed a condition called "Cherry Eye".

Dogs actually have three eyelids. The third eyelid is difficult to see but it contains a tear gland which sits inside a little pocket on the back of the third eyelid  and this gland helps to produce tear fluid.

Without tear fluid, the eye becomes dry, uncomfortable and at risk of damage. I suspect that the bulge you see in the eye is this gland that has come out of its pocket in the third eyelid. This can cause the eye to become more irritated - It can also affect the tear production in some cases.

The cause of Cherry Eye is not known, but it is thought to be due to some dogs having a weakness of the tissues that holds the gland in place. Certain breeds are more predisposed than others. It is not unusual for dogs that get Cherry Eye in one eye to also get it in the other eye.

Because of the possible severe consequence of the function of the eye - if this condition is not corrected - I would recommend that you contact your local vet to get the diagnosis confirmed, and discuss with your vet the possibility for an corrective Cherry Eye surgery.

The prognosis for surgery with regards to this condition is good, but relapse can occur.