Only you know deep down if you are an alcoholic. From what you describe, you are certainly abusing alcohol.
Experiencing any sort of withdrawal is a VERY bad sign.
A good way to find out if you have a problem is to just stop, if you can't... there's your answer.
The sooner you can break through denial, the sooner things will get better. Everyone here gets what your going through and if you come to the conclusion that you have a problem, we'll be here to help.
Welcome anewpage!