You should wash your eye with clean water which will help remove any foreign body which might have gone in your eye. It might be infection too, so look for any accumulated discharge and sticking of eyelids in the morning, if yes, then start antibiotic eye drops (moxicip) 4 times a day. If there is no discharge and watering persists then you should start antiallergic eye drops (olopatadine with ketorolac) three times a day. In case after using anti allergic or antibiotic eye drops (depending upon the situation) for three days if the watering does not decrease then you must see an ophthalmologist.
Next Steps
Get your syringing done by an ophthalmologist.