Yes, she most likely has an eye infection. I wouldn't use over-the-counter eyedrops for any animal. Best to take her to a vet promptly. If it's just an infection, she'll be given antibiotics. Not too expensive, if it's caught early.
Check your husbandry as well--make sure the temperatures are correct, and that her insects are gut-loaded well, and dusted with calcium. Use a multivitamin powder once a week, instead--it should have some preformed vitamin A.