It's impossible for me to answer this question simply because I don't know the specifics of the accident. Furthermore, the only people that can determine fault are the specific claims adjusters assigned to this claim. This kind of situation can be tricky because an insurance company will usually be on your side and negotiate these situations for you. I would get the contact information for the other driver's insurance companies, the claims adjusters, and potentially seek legal advice, if necessary.
If you do get a new car in the future, make sure you get insurance
for the vehicle and stay complaint with your state's car insurance laws and regulation.