My Son Is 10 Weeks Old And Has Had Gunk

My son is 10 weeks old And has had gunk in his eye all day and it's been watery. I called doc and he prescribed fucithalmic but told me not to give it to him unless it got red or crusty. His eye is now pinkish and when he wakes it is crusty. Should I fill prescription? I don't want to give him something he doesn't really need,