I'm sorry to hear about your accident.
There are a couple of things to think about here. First, you'll more than likely have to alert your insurance company. Any time there is damage to your vehicle, they will usually require you to report it. In this case, your insurance company can be helpful considering the mechanic might be responsible. If that is the case, the mechanic's liability coverage would provide you a settlement.
As for the total loss, this varies by state. For New York, a total loss is determined by a "Total Loss Threshold" of 75%. Meaning, the value of damage needs to be at least 75% or more in order for the vehicle to be totaled. Using your estimates, it's likely your vehicle will be totaled.
If you're not willing to contact your company, you could take the settlement and try to repair the vehicle. In this case, you would have a salvaged title which could impact your ability to get insurance. Most insurance companies view a salvaged title as a bigger risk factor than a non-salvaged title.
Best of luck. Below are links to some information related to total losses/salvaged vehicles and claims: