You’re absolutely right that you can’t write a character as just an addict, and yes, addiction does take over a life. I haven’t ever written addiction, but I’ll give this my best shot. You should definitely write about the struggles that your character faces, but more than that, dig deep. How do they feel? What are they thinking? Do they feel guilty for being this way? Sad? Angry? What drove them to drugs? When did they know they were addicted? Can they admit to themselves that they are, in fact, an addict?
You should also focus on relationships. If they’ve just done drugs, they’ll probably react differently to certain things than they would when sober. What happens when other people realize what’s going on? How does it affect their relationships with other people? What about love?
Remember that addicts are people, too, and they have lives and hobbies like everyone else. Sometimes those things get pushed to the side in pursuit of the drugs, but they’re there. Does your character have a job? A sport they like to play, or some other activity they like to do? What makes them happy that isn’t the drugs? What else is going on in their lives?
Those are the questions I ask myself when writing mental disorders so that the disorder doesn’t dominate the character. People live with addiction every day. But they’re still just that: people. So instead of focusing solely on the addiction, remember to explore feelings, relationships, and daily life. Focus on what makes them a person, not an addict.
I hope that helps, and good luck!