Can I still drink socially only and be an alcoholic?

Possibly. Ask yourself these questions: 1) do you feel the need to cut back on your drinking? 2) are you annoyed when others ask you to stop? 3) do you feel guilty about drinking? 4) do you need an "eye-opener" drink in the morning to get going? More than one 'yes' response to any of these questions raises suspicion of alcohol abuse.
Yes. If you have had serious alcohol problems in the past to the point where someone thought, or you thought that you were alcoholic, then it is unlikely that you could continue to drink in some controlled or "social" fashion for very long. In addition, i don't know what you mean by social drinking only. I have had patients drinking 1 1/2 liters of vodka a day and called it social drinking. Get help.
What is social use? Only about 5% of alcoholics fit the profile of a "skid row bum". Alcoholism can present in many ways. Virtually ever alcoholic I have treated initially described them self as a social drinker.