My left eye hurts and underneath the eye is puffy?

Multiple causes: Sudden soreness and swelling of the eye or eyelids can have multiple causes. Most common would be a chalazion or a hordeolum (stye). Other infectious and inflammatory causes are possible, including conjunctivitis, iritis, sinusitis, etc. You can try a warm compress (clean washcloth rinsed with very warm tap water) for a day or two, but see an eye md promptly if the symptoms are not resolved soon.