Can allergies cause your eyes to hurt and for you to feel tired?

Yes... Allergies can cause symptoms as you describe so see your doctor so this can be diagnosed and treated.
Occasionally. Eye allergies can cause itching, watering and discomfort. Artificial tears, antihistamine eye drops and cool washcloth compresses can relieve the symptoms.
Yes. Artificial tears or allergy drops may help with the symptoms.
Not specific. Allergies make your eyes itch. Painful eyes can be a symptom of many illnesses - some more serious than allergy - viral meningitis, for example. The same goes for feeling tired. This is a known but uncommon symptom of allergic rhinitis. Infections can also make you feel tired. Symptoms that persist for several days or are getting worse are best handled by seeing your doctor promptly.