I "suspected" I had a problem when I decided to stop drinking (after a really bad bender), and had terrible withdrawals and couldn't stay stopped for more than 3 days.
I also suspected I had a problem when I started turning down social engagements in order to stay home and drink alone.
I realized without a doubt that I had a problem when my body officially became addicted to alcohol and I couldn't go more than several hours without a drink. When I was forced to maintenance drink every few hours or so, the real horror of my situation hit home.