First of all, you’d better use topical eye drops containing antihistamines indoors, which can help stop your eye from reacting to allergens such as dust, pollen and pet dander. Then when going outside, sunglasses should be the must-have to protect from UV.
Sunglasses can help to avoid spreading conjunctivitis, but I suggest not go out during this period. It sometimes needs medical treatment like anti-inflammatory drugs and special eye drops.