My left eye is pinkish, extra teary and looks a little swollen underneath. Does that mean infection?

Likely. Most common eye infection in adults is viral cause. Viral cause starts in one eye. But because it is contagious it often involves both eyes. Antibiotics do not help, but some physicians use them to treat or prevent a bacterial conjunctivitis. Viral conjunctivitis resolves on its own most of the time. Rarely do we intervene with antivirals. If gets worse see a physician.