It depends. Conjunctivitis can be allergic, inflammatory or infectious. There are no home remedies for infectious or inflammatory conjunctivitis, while occasionally cool compresses and artificial tears can allevieate some of the symptoms of the allergic form. It is important to find out which type you have in order to treat it properly. For this reason, you should have an eye doctor evaluate your eyes.
Blepharitis. Conjunctivitis is a broad term meaning redness and irritation of the eyes. The most common chronic causes are blepharitis and dry eye. Acute causes include infection and allergies. Since the causes are so varied it's best to see your ophthalmologist or primary care doctor to they can sort through the common symptoms and help you. Cool artificial tears can help till you get seen.