I thought DD had pink eye at 6 weeks old b/c her eye was veiny & crusted shut, but luckily the pedi said it was just a clogged tear duct. It cleared up in 3 days by just applying warm compress, massaging with my finger in a downward motion along the side of her nose & suctioning.
Like the PP mentioned, when my son had pink eye, he also had an (double) ear infection. He was given antibiotic for the infection & drops for his ear.
Hope LO feels better soon!