Closer to the end of the series, he basically loses his mind and is destructive to himself and others. An entire plot line was House hallucinating that he had quit and recovered from withdrawals (among other imagined or altered events) only for it to be revealed that he was using more than ever.

So, he canonically has more problems with drugs than social disapproval.

> He goes cold turkey a couple times and proves that he's in actual pain.

This doesn't contradict the fact that he's an addict, which is clearly portrayed in the show from the very beginning.