If someone’s name was wrote down as an emergency contact or on your insurance do they have to right to your health information

So my parents kept demanding me to go to doctors insisting I’m ill. It’s because whenever I confront them on something that they know happened they want to start yelling at it, claim they don’t cry anymore, they’re living on cloud nine and nothing can stop them, etc. When I saw the doctor they tried to give me something and I took it to shut them up which they started using it against me claiming it’s proof I’m ill and if I don’t have anything I’ll die. When I was seeing the doctor I wrote my father down as an emergency contact and he gave me his insurance card to use so I used it. After when I called the doctor and told them I had a bad reaction to the medication they started getting belligerent with me and yelling about it saying “I won’t let it work” meanwhile I tried to explain to them sometimes it just doesn’t work. My father was yelling at me “if my name was wrote down as an emergency contact or if I’m the insurance carrier can I get the information?” Which I told him no you can’t because I didn’t sign for you to allow it he got mad. It seems as if my “father” was worried I could be saying something against him and he wants to know so he can try to hide it and save his ass. I’m saying this because he was wrote down as a perpetrator for child abuse and murder a few times.