Should I take my pain pills for my pulpotomy?

I recently had a pulpotomy (emergency procedure, they didn't even tell me until they finished b/c I hate the dentist) and they proscribed my some hydros. I still live with my parents, I'm 18, and they don't want me to take pain pills b/c dad is a cop and sees how people can get addicted etc. anyways, I'm not having a terrible amount of pain, until I drink a cold drink. It is the worst pain I have felt in my mouth, and I've even had dry socket in all four sockets from wisdom teeth. This pain is sharp and feels as if someone shoved a knife in my gum and is dragging it back and forth the length of my tooth, almost making me cry each time. Anyways, does this pain qualify enough for a pain pill?

Thanks in advance.