My dog's leg as lacerated at daycare and he had to undergo surgery. The daycare is paying for the vet bills, but can I still sue for other damages?

My dog's leg was lacerated while he was at daycare. The hole in his leg is huge and the muscle was showing. The daycare employees notified me and offered to take him to the vet if I wanted them to, but told me it didn't seem like that bad of an injury and would probably heal on its own. I go to pick him up 3 hours later and they said it hasn't stopped bleeding (I asked them to update me if I needed to come get him sooner if his leg got worse, which they failed to do) but insisted that it would probably heal on its own. I still took him to the vet, who was appalled that they had downplayed such a serious injury. My dog was immediately admitted for emergency surgery. Daycare offered to pay all vet bills. However, I had to leave work early and am taking time off to care for him and take him to his follow-up appointments. He is pain and is not sleeping at night, meaning that I am not sleeping at night. This whole thing has been very emotionally distressing. Can I sue for other damages?