Will I need to sue my HVAC contractor?

The company policy about animals in the workplace was very clear.

Since I was attacked and bitten by a dog while in the course of my duties, I feel entitled to sue for damages. What happened was not my fault, but I seem to be the one paying the price for it. When clients sign up for our annual service plan, they have to sign a contract. Part of that contract is an agreement saying that all pets and animals need to be restrained when an HVAC service tech is on the premises. The dog doesn’t have to go in a cage, but it should be secured in another room so it can’t disturb the HVAC worker. Since this client signed the contract that meant they were legally responsible for my medical bills. The HVAC contractor does not offer very good medical insurance, and I had to pay a lot out of pocket to deal with the dog bite. Not to mention the fact I had to miss two weeks of work after the incident. The HVAC contractor asked me not to sue the client, because it would make him look bad. Meanwhile he won’t pay my medical bills, either, so what choice do I have in the matter? I had been attempting to repair a faulty valve in the water boiler when the dog attacked me. If the client won’t help me, and the HVAC contractor won’t help me, then I hope the justice system will have my back! If the HVAC contractor fires me because of it, I’ll sue him, too.

a/c professional