The condition looks infectious. You need to start antibiotic eye drops. Start moxifloxacin eye drops 6 times a day with regular cleaning of eye with Luke warm water. Also because the condition is persisting for a few months, it could be due to nasolacrimal duct obstruction. That can be confirmed by a simple test by an ophthalmologist, but only after active infection is over.
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If no improvement in a week, consider consultation.