I think your natural composition skills are unusual, but not unique. I also begain to compose music at a very early age. My knack for picking melodies up out of the air and playing them on a piano when I was 7 years old was how my parents knew that I needed lessons. Naturally, I was surprised later in life to learn that other people had to learn basic things like pitch and rhythm; to me it had always been just as natural as speaking.

I believe the same is true with song writing, in a sense. You're still applying some parts of music theory, but most by-ear learners like ourselves simply grasp the concepts and have internalized them naturally, without needing to be taught. Music is little more than patterns at the end of the day, and our brains are very good at recognizing patterns. What you and I know intuitively, others can learn through training and repetition. Both approaches are valid, and yield interesting (and often different) observations.

I went going through Music Theory classes during my brief adventure with Liberal Arts Majors in college. I felt like I already "knew" the material in a way I couldn't quite put my finger on. It was like I was finally understanding what my brain had been doing all these years. I recommend it if you haven't yet had the experience.