That depends! You can find the reason which caused the sore eyes. If the sore eyes are caused by infection virus such as pink eyes, it may spread and contagious. But if it is caused by fatigue or trauma, it has no chance to be contagious. Check your eyes with the doctor, and then you can decide to go out or at home!
Sore eyes are common terms used for conjunctivitis or pink eye. It refers to the inflammation of the cornea, the clear and transparent membrane covering on eyeball and inner the eyelids. With a sore eye, you might have increased sensitivity to light, pain in eyes, grittiness, redness and watery of eyes. The inflammation might caused by bacterial infection, viral infection and allergic reaction. As to allergic conjunctivitis, it is not contagious. As long as it is not serious and you are now getting out of touching with the allergens, the symptoms would clear out soon. But as to bacterial and viral infections, it is highly contagious. It would be better to say at home if you could. Have a good rest and take some home remedies to help the sore eye healed up faster. Applying warm compress on eyes would be good treatment for sore eyes. You can also try some drops to help control inflammation like breast milk, salt water, baby shampoo and so on.