Is addiction a spiritual or a medical problem?

I'm assuming your question is about whether addiction is a spiritual or a medical problem, and that your decision about the kind of treatment you need will be based on the answer to that question.

My problem with your question is that it divides the human being up into segments that were never meant to be separate.  We are whole beings, and our spirit, soul, mind and body are all contained in our skin.  Recovery from substance abuse involves every part of our being submitting to change, not just isolated parts of us.  When I use drugs I make the decision with my mind and everything else agrees to go ahead - my emotions, my spirit, my soul and my body.  All are present and active.  When I choose recovery, every part of me needs to choose it, or I won't succeed.

And usually I need help for that, because even though God gave me a perfectly good brain, when it's immersed in an addictive cycle it doesn't decide the best things for me. This is why the first two steps of the 12 step program acknowledge our powerlessness and elicit the aid of a "Higher Power", and whether the person in the program has ever embraced spirituality or not, the program won't work for him unless he does now. 

I'm not sure what you mean by "science and medicine" based treatment as opposed to "Christian treatment", as both AA-type recovery programs and Christian recovery programs use the same 12 steps.  Sometimes one needs to check in as an in-patient because using an external program is not working for them, due to factors such as still being in the locality where associates and drugs are presenting themselves daily, etc., but even as an inpatient the 12-step program is usually followed.

Part of being on a 12-step program is having an accountability partner, or sponsor - someone you are completely honest with. This idea has a biblical foundation; there are many places in the Bible where it says we are to be accountable to God and to one another (Rom 14:12, Gal 6:1-2, Thess. 5:11).  As well, a sponsor is a wonderful source of support when the going gets tough.  Finally, the idea of "science and medicine" as a fix for addiction sounds like just that - a "fix", whereas real recovery takes a lot of time and hard work in order to be achieved, and all that work is done by the person who is recovering, not the doctors and nurses around him.

I wish you all the best with your desire to change your life for the better.