Yes I do have a drinking problem, but I am also a problem drinker. I am an alcoholic,
Killswitch: it sounds to me like you aren't sure what you are! And, it is not at all strange to be unsure if you are a heavy drinker or an alcoholic. I would suggest you read the stickies here on the site to make a decision about what you are.
You can also take some online tests. You can learn about the stages of alcoholism and see if you can spot yourself in one of the stages. There is actually a lot to learn about the disease and despite being an alcoholic, I can honestly say I knew practically nothing about it when I first began to think about quitting.
Nobody can tell you if you are an alcoholic or not. Lots of people hope they can go to the doctor and get a diagnosis. Most can't, unless they have reached chronic stage and/or their physical health is compromised enough to show clear symptoms. I was a daily drinker plus a binger, (it wasn't pretty), and I did show some elevated liver levels, but nothing alarming. Ultimately, it wasn't my test results or discussions with my doctor, it was my inner decision and acceptance of the fact that I am an alcoholic.
Part of me still tells myself that I can handle it, and I can moderate,
Yup.