Getting a quote from a repair shop won’t automatically start a claim with your insurance company. However, since the damage occurred years ago, your insurance may deny the claim because you didn’t notify them in a timely manner. Comprehensive coverage typically covers this kind of damage, but it’s unlikely to be honored after so much time.
New York’s statute of limitations for property damage is generally three years. Since the incident happened in 2016, it’s well past the time limit to file a claim. Unfortunately, you won’t be able to collect anything from your insurance now.