Hi,
I understand your distress. It is an adverse drug reaction to sertraline. It has anticholinergic effects which is responsible for the dry eyes. In your case, you dont wanna change the dose or the drug the only possibility remains is to visit an ophthalmologist for a better variety of tear drops (multiple varities available) which can help you with dry eyes and yes this increased blinking is a reflex action to dry eyes. And at last i need to say that the anticholinergic side effect decreases with time but the effect persists or get better with time.
Next Steps
consult an ophthalmologist