Drug addiction

Do you think drug addiction is a disease, or just a choice?

Addiction by definition is a disease, or at least a condition.
As long as it's a choice, it's not an addiction.

It starts as a choice and turns into an addiction.

"Addiction" (or, medically, a "Substance Use Disorder") is much to multi-faceted to be pigeonholed into choice or disease. The medical community has long had the most influence over how it's viewed with the official stance of the National Institute of Drug Abuse (U.S.) declaring it a "chronic, relapsing brain disease". Much of the funded research follows suit to support this view.

Researchers who point to more of a neurobiological influence - and the ability of the brain to adapt to new stimuli - are often the bane of the NIDA since these other researchers will state plainly that addiction is NOT a disease, although there are brain/body influences. However, these are not the only factors. - This is where I stand, personally

These "other factors" can include developmental and chronic trauma, early attachment trauma, Adverse Childhood Experiences (ACES), social determinants of health, and others. The brain is also very adaptable. When new learning takes place - when the brain essentially "re-learns" (so to speak) what is healthy, pleasurable, and rewarding in recovery, this new learning helps to form new neurological pathways in the brain that can interrupt the "chronic, relapsing" nature of the disorder.

So, no I do not believe that addiction is a disease (I did at one time)
Choice...? That question is much to nuanced to really answer with yes or no