NicMM: I just sent you a PM with some real-world experience. You need to think back of what papers you signed at the hospital. Most likely they were for a next of kin authorizing care. However, they could have been about assuming financial liability. OTOH, if you signed with your dad’s name… then maybe you’re already off the hook.
I remember reading something about a teenager (maybe pre-teen) who had an accident, not life threatening, and was taken to the ER by his grandfather. When the hospital staff asked the old man “who is the (financially) responsible party?” he pointed at his grandson and said “he is!” That was a smart thing to say, by the way. In this case, the ER staff proceeded to stabilize the patient and grandpa didn’t have to worry about paying anything.