Bacterial pink eye is treated by repeated warm washcloths applied to the eyes (try applying these to your child's eye one eye at a time during a favorite video) and requires antibiotic eyedrops or ointment prescribed by the doctor.
I do not believe you'll be able to get free antibiotics - however you might try a clinic in your area.
You can call your local community health center. They will have clinics in your area that work on a sliding scale often times they also have pharmacys that work on a sliding scale as well. If they do not have a pharmacy they may have samples they can give your and or be able to prescribe you with a generic brand of drops that you can get at the pharmacy for very low cost. Many pharmacys have programs where they offer thousands of generic brand prescriptions at very low cost. Walgreens is one of those pharmacys