Other driver turned into your lane without looking, no question.
Police report? Should have been called.
Is Texas a no-fault state? In which case, you call your insurance company. Then you let your insurance company duke it outwith the other insurance company; believe you me, insurance companies are much better equipped to duke it out with each other than for any individual to try and get blood out of a stone from the other insurance company.
Besides, not calling your insurance company after an accident can invite some serious problems, especially if the contract you signed with your insurer requires you to make immediate contact. (Yes, an insurance policy is a contract. Both judges and arbiters take a very dim view of violating the terms of a contract.)
In NJ, a no-fault state, when something vaguely like this happened to me some years back, my insurance paid for the repairs and all except for the deductible. Then, when the other insurance company admitted their driver was at fault a month or so later, I got a check in the mail from my crowd for the amount of the deductible. And my insurance company made a point of saying my rates weren't going to change as a result of all this, since it clearly wasn't my fault.
Now, many, many moons ago in Indiana, where I was going to college at the time, one snowy day caused an interstate off-ramp in the middle of farm country to become covered with glare ice. I figured this out when touching the brakes resulted in No Action At All, followed by frantic manual brake pumping (long before antilock brakes were common) for several hundred yards, finally slowly decelerating to a halt a hundred yards before the end of the ramp.
Hyperventilated for a few seconds, then looked in the rear-view mirror: Here comes some older guy in a Big Car with this look on his face, "Geez, why did that guy stop right there?", followed by him turning the wheel to go around me and, of course, his car continuing on its merry way with nary any change in direction and ramming more poor college econobox in the rear. It was driveable, but the bumper was badly banged up. the trunk would close.. barely. and it drove funny.
Open and shut, right? He got me. But Indiana, at the time, was a, "fault" state, and State Farm, his insurer, decided that paying a poor as blazes college student wasn't in the cards. First, the old fart had to file a police report. (There already was one.) Then he had to file a statement. Then paperwork had to be processed. The accident happened in February; by the time school let out in May for the summer, they still hadn't paid.
Then California, the state where I had a summer job, occurred. After managing to get over the Rockies, got settled in, and gave the State Farm branch over there a call, asking, "Well, I've been working with your branch in Indiana. I'm here now. What do I do next?".
The voice on the phone politely took my claim numbers and such and started to sound more and more agitated as the details sunk in. After getting my land-line number (no cell phones back then), she forecefully ordered me to stay on hold, not go anywhere, and wait.
Five minutes later she and another person got on the line, and ordered me to take the car to some State Farm service center. Immediately. Like, this second. Go!
Got in the car, limped over to this place a few miles away, and some adjuster crawled around under the car for a few minutes, popped out, filled out some paperwork, and told me to Call This Number in a couple hours.
Feeling that I'd fallen into some kind of whirlpool, called back. Was told to take the car to an auto body shop ASAP and was given a new claim number. Got them to give me the name of such a body shop (I was really, really new to CA), which they did.
Car was fixed in, like, three days, new bumper, frame straightened, and all. I didn't have to pay anything.
As I said, CA happened. Turns out that then, and I believe still now, CA's department of consumer protection has the habit of setting up oddball damaged cars under weird (but fake) circumstances, then plopping these situations upon insurance companies, repair shops, and the like. Rumor has it that they have spiders on staff to leave cobwebs and the like in places on the gear/cars/whatever so it's not obvious that this is happening. You know those auto repair places where, after sizing up the customer and, if they're ignorant enough, they get told that, on top of everything else, they desperately need a radiator flush for $1000, or the car will break down? Those people (and, we're talking dealerships, not just a crooked idiot mechanic on a corner somewhere) get shut down for months for those kinds of shenanigans. Repeat offenders get shut down, period.
In the face of this, repair shops, insurance companies, and so forth, when faced with, shall we say, somewhat shifty situations tend to overreact madly. Nice, if one is a consumer.