Could be Nasolacrimal duct obstruction (NLDO) .
Next Steps
Keep giving Nasolacrimal duct massage as per this link.: https://www.nationwidechildrens.org/family-resources-education/health-wellness-and-safety-resources/helping-hands/eye-tear-duct-massage
Health Tips
Since it is 2 month of age... should also be seen by pediatric ophthalmologist.if you want you can search on practo or contact me .