You cant. If it's viral (most are), nothing will alter its course. If its bacterial, antibiotic can shorten course by a few days.
Viral infection. Classic pink eye results from adenovirus or rhinovirus, and is self-limited. Should clear without treatment in 3 to 7 days. Antibiotic drops only help if bacterial component, usually accompanied by yellow mucus discharge. Itching and redness of viral conjunctivitis can be relieved with otc antihistamine-vasoconstrictor drops like naphcon a. If symptoms last longer than 5 days see eye doctor.
Self limited. Pink eye is self limited, just make sure your one year old does not have clogged tear ducts. In a one year old this could mimic pink eye. An ophthalmologist should exam your child to rule this out as well as more serious conditions if this persists.
See the Eye MD. You should take your child to the ophthalmologist. You have to determine the cause of the conjunctivitis. Does you child wear contact lenses or have allergies? They are treated very differently. For comfort you can start with luke warm compresses twice a day. Also you should have our child do frequenty hand washing and use paper towels instead of cloth towels to dry hands.
Usually can't. Pink eye is a common term for viral, bacterial or allergic conjunctivitis. If its viral, it will resolve on its own, but artificial tears may help. Bacterial needs to be treated with antibiotics, and allergy can be treated with antihistamine/mast cell inhibitors. Have him see an ophthalmologist to find out what he has.