I'm assuming you didn't get a police report. If you did, once that is provided to the at fault insurance company, things will go smoother but not without a lot of work on your part.

I just learned this as my son was in an accident that totaled his grandfather's truck.

He turned left on a protected arrow and a lady, previously stopped at the red light, decided to go and hit him, spinning him 180 degrees.
She told the POLICE that she didn't know what color her light was.
She filed against my insurance and told MY insurance that my son took the turn too wide and hit her. Physics would prove this impossible.
When I filed against HER insurance, she told her insurance that my son ran a red light and hit her. Also impossible due to how the impact occurred and where the vehicles came to a stop.

Lucky for us, there was a witness who stopped and gave her info to the responding police. The police report stated that she was at fault.
Then, and only then, would her insurance engage.

Even at that rate, I had to fight HARD to get the amount I wanted for the totaled vehicle. And my son wasn't injured in the accident but I still fought for pain & suffering.
And when GEICO told me that my son's mild injuries and missing school due to back pain, and that we were now without a vehicle that we relied on for transportation were all INCONVENIENCES, I about lost my mind.
Told them I was contacting an attorney.
They called the following day and asked if I had contacted an attorney yet. I told them not yet, but will that day. They started the offer process.

It's a PITA.
Good luck.

There are some decent articles on the www about how to negotiate with insurance companies. I read a few and took some advice that applied to our case and I feel that it helped.

Alright.

I called my insurance agent. She told me I can file a a claim against my insurance, get everything fixed, but I will have to pay my deductible.

If the at fault drivers insurance accept fault, they will pay all costs, she talked can’t a subrogation process, where they get everything back including what would be my deductible, but this could be anywhere from right away or months or longer.

Does this sound right?

I had the same experience with Allstate. Their client backed into my car in a parking lot as I was driving down the row between spaces. $2,500 damage to the side of my car. The woman and her husband apologized and I got their insurance info. They asked me to get a repair estimate before I called their insurance in case they wanted to pay me directly. When I did contact Allstate they said their client claimed I hit them and they were not even moving. I asked the insurance rep to explain how I would have hit the back of their car with the side of my car and she admitted it sounded implausible, but because their client denied fault they would not cover my damage. That cost me my $500 deductible. Vowed to NEVER do business with Allstate.

Did you tell him you were recording? Or do you have to? I don’t know the laws on that

I had the same experience with Allstate. Their client backed into my car in a parking lot as I was driving down the row between spaces. $2,500 damage to the side of my car. The woman and her husband apologized and I got their insurance info. They asked me to get a repair estimate before I called their insurance in case they wanted to pay me directly. When I did contact Allstate they said their client claimed I hit them and they were not even moving. I asked the insurance rep to explain how I would have hit the back of their car with the side of my car and she admitted it sounded implausible, but because their client denied fault they would not cover my damage. That cost me my $500 deductible. Vowed to NEVER do business with Allstate.

not in texas

Alright.

I called my insurance agent. She told me I can file a a claim against my insurance, get everything fixed, but I will have to pay my deductible.

If the at fault drivers insurance accept fault, they will pay all costs, she talked can’t a subrogation process, where they get everything back including what would be my deductible, but this could be anywhere from right away or months or longer.

Does this sound right?

This is why I have front and rear dash cameras in both my vehicles.

No one asked or cares about your cameras.