My family thinks I am an addict, but I don't agree. Whose right?

Probably them. Most addicts have very strong defense mechanisms. Denial, literally they just can't see the problem.They justify, minimize, rationalize, intellectualize, lots more " izes". One component of addiction is conflict with others. I don't know you, so all I have is my knowledge of how addiction works. I recommend finding a local counselor or other professional to help all of you figure it out. Good luck.
Family disease. You are all right. Consider attending a meeting of al-anon together and consulting a professional experienced with families and addictions.