I would still use the eye ointment, since it may soothe the eyes. Bausch and Lomb Eye Relief Eye Wash (about $5) is also very good for irritated eyes instead of the antibiotic ointment. Here is what it looks like:
https://www.target.com/p/bausch-lom...x4fdlCHbVcoQondj7mBoChzIQAvD_BwE&gclsrc=aw.ds
https://www.target.com/p/bausch-lom...x4fdlCHbVcoQondj7mBoChzIQAvD_BwE&gclsrc=aw.ds