(The OP's other thread states that she's in Georgia [assuming that Heorgia means Georgia])
If you can't get compensation from the groomer, then yes, you would need to sue them.
How do you intend to prove they caused the injuries?
How long was the dog at the groomer? It seems strange to me that a dog can go in the morning with perfectly healthy ears and come out a few hours later with infected ears. Infections usually take a little longer than that to set it...