Insurance companies have shops they work with to make the claims process go easier. The shop will examine your car and make a determination of what is needed to put your car back into the condition it was in just before the crash, unfortunately this process does take time
In September my van was legally parked in a strip mall when a small car whipped around hit another van and hit my right rear tire at an angle. If I had a spare tire I would have changed it and driven it home. The damage seemed to be cosmetic. It was towed to an impound lot and a week later to the other persons insurance companies prefered shop ( a well respected shop) It took 4+ weeks for the shop to look at my van (I was offered a rental by the other insurance company) Their initial estimate was $8k and the van could be fixed, once they dug into it some more they found the rear frame was bent and could not be repaired and meet industry standards. The van was totaled and I got a fair settlement.
Be prepared for delays as most shops are backed up.
If a repair shop can’t get to it right away, get your car checked out by your regular mechanic to make sure it can be driven safely, that may be on your dime but well worth the peace of mind