What could be causing my eye pain and sensitivity when I touch my eye?

Eye pain. Eye pain can be caused by many entities-- dry eye, allergic conjunctivitis, corneal abrasions are common causes-- viral conjunctivitis can also cause eye pain-- if artificial tears do not help, you should see an ophthalmologist to have the eyes checked.
Many things. Could cause these symptoms, many of which are serious and should be evaluated by an ophthalmologist.