Answers: I think your asking in the order of the herb, not the essential oil. (Don't put essential oil in your eyes.) Chamomile have mild antibiotic actions so it may give a hand conjunctivitis. Here is the info for herbal use I found on Univ. of Maryland Med Center site:
Alternative therapies can oblige relieve your symptoms. You must, however, be careful that any solution or compress you put on your eye is sterile. Remember, too, that you can spread conjunctivitis from one eye to another, so avoid your other eye while treating the artificial eye. If you have a mild crust of conjunctivitis, begin next to compresses. For a moderate case, use a compress and an eyewash. Many those find relief beside a boric acid eyewash or compress. Boil 1 tsp. boric tart in 1 cup dampen, cool, and apply with a sterile eyecup or washcloth.....
Herbs
Herbs may be used as dried extracts (capsules, powders, teas), glycerites (glycerine extracts), or tinctures (alcohol extracts). Compresses and eye wash are external treatments. You can make a compress next to a clean cloth, gauze pad, or cotton balls soaked within a solution and then applied over the eyes. You can apply eye wash with an eye cup or a sterile dropper.
Compress: Use five drops of tincture surrounded by 1/4 cup boiling water or steep 1 tsp. herb within 1 cup boiling water for 5 - 10 minutes, strain, and cool. Soak cloth or gauze within solution, and apply over the closed eyes for 10 minutes, three to four times a day.
Eyebright (Euphrasia officinalis): help fight infection and dry up excess fluid.
Chamomile (Matricaria recutita): help fight infection.
Fennel kernel (Foeniculum vulgare): helps come to blows infection.
Marigold (Calendula officinalis): soothes irritation.
Plantain (Plantago lanceolata, P. major): astringent and soothing. The fresh leaves are the most effective plant quantity.
Flaxseed (Linum usitat issimum): as a soothing poultice made with 1 oz. of bruised flaxseed steeped for 15 minutes contained by 4 oz. of water, wrapped contained by cheesecloth, then applied directly to the artificial eye.
Grated fresh potato has astringent (drying and disinfecting) properties. Wrap contained by cheesecloth and apply.
Use above herbs singly or surrounded by combination: Mix equal parts together then steep 1 tsp. herb surrounded by 1 cup of boiling water to form a tea. Cool before administering to the eye.
I assume you anticipate Chamomile tea rather than essential grease. The purpose is to soothe the irritated tissues surrounding the eye.
USE CAUTION...There are at least 3 plants that are botanically different that are call Chamomile. Know which one is advised and which you are using. The tea should lone be used as a compress on a closed eye. Do not use as a wash for the eye. Be aware that in that is a possibility of allergic dermatitis associated with the use of Chamomile tea as a compress.
Never put anything surrounded by your eye that is not intended to turn there. A commercial eyewash if fine because it is sterile. If you mix it beside herbs or anything adjectives bets are off. People hold gone blind puting home remedies in their eyes. Better to own an infection then the entail to walk beside a white cane.