What to do if I got into an auto accident a few weeks ago and the shop that I brought my car to inflicted damage to my car?

You can sue the auto repair shop for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable auto repair shop would have exercised under the same or similar circumstances to prevent foreseeable harm).  In order to prove negligence, you will need to prove duty (of due care mentioned above), breach of duty (failure to exercise due care), actual cause, proximate cause and damages.

Actual cause means but for the auto repair shop, would your car have been damaged?  If the answer is no, actual cause has been established.  Proximate cause means are there any unforeseeable, intervening acts which would relieve the auto repair shop of liability?  If the answer is no, proximate cause has been established.  Damages means the amount of compensation you are seeking in your lawsuit for negligence.  Damages would be the cost of repairs to your car.  If you need a rental car while your car is being repaired at another shop, your damages should include the cost of the rental car.  You will need to mitigate (minimize) damages by having the repairs done at a repair shop whose charges are comparable to other auto repair shops in the area.  If you were to select the most expensive auto repair shop you could find, your damages would be reduced accordingly for failure to mitigate damages.  The same applies to the rental car.  You will need to select a rental car with a reasonable rate.  If you were to select the most expensive rental car you could find, you would have failed to mitigate damages and your damages would be reduced accordingly.

In addition to your photos of the damage caused by the repair shop, additional evidence to support your negligence claim could include a statement signed under penalty of perjury by the repair shop you select to repair the damage from the first repair shop stating the specific damage that was caused by the first repair shop.