Good to see you again FD.
Inpatient rehab may be a great thing right now for you. It will put you in a safe environment away from temptation. Please consider it.
You, too, can have a life of freedom from the slavery of alcohol addiction. I can feel the pain in your post because I was there less than 2 months ago, but today I am free. This can be true for you also.
Please don't give up on the sober life that you deserve.
Also, your counselor seems to not have a clue about what alcoholism is. A lot of alcoholics never drank in the morning. Whether or not you drank in the morning doesn't determine whether you have alcoholism or not.
It doesn't matter what time of day you start drinking, if you have one drink and then lose control and can't stop and crave more, then this is a sign.
Please consider the inpatient rehab. It would be good to have that medical care while you detox and be in a safe environment to get a head start on your recovery journey.