Hi,
How is your son? Are there other symptoms present like fever? Eye infection may indeed be due to conjunctivitis- which can be caused by irritation, viral or bacterial infection. It is best that you have this checked by your doctor for proper evaluation. Direct clinical examination is important. Try to wash your hands regularly and to cover his hands to prevent him from touching his affected eye. Take care and do keep us posted.
Unfortunately conjunctivitis can be viral and if it is viral then it has to run it course much like a cold would. It is like having a cold in your eye. However, your baby is very young so err on the side of caution and make a doctor's appointment if you feel it is not getting better.