IEEs are not all that social and happy I would say. I They are often described as the most shy of the extroverts. I listened to a lot of Doors growing up, never had a large social circle, am only exuberant and happy when I feel very comfortable with people, and can be very withdrawn and a loner at times. I very much think you are an IEE based on what you write here.
Oh, and abandon MBTI - it is terrible! Welcome!