Yes, I believe in inner worlds. I have one myself. Let's think about your very vivid inner world, though. Wouldn't you agree that it wouldn't be possible for your inner world to exist in the way that it does without the external world? How could you speak English if you hadn't learned it from somewhere outside of yourself? How could you read books if they were not written by someone else? If there wasn't an outer world, what would you think about when you escaped from it, your heart beat? How could you contemplate who you are if you had nothing to compare it to?
I don't understand your last paragraph because I completely agree with what you said, and I don't think I said anything to suggest that I do not. I also never said that I don't think inner worlds don't exist. If anything, inner worlds are all that exist. And yes, introverts do feel drained from too much socialization. I never said they didn't, mostly because it has nothing to do with what I was talking about.
I only have one reality, and it's internal. I think it would be very inopportune for me to cut my reality in half and then favor one half over the other.
But I assume nothing. I just like thinking and figuring things out. If I am an extravert, it certainly does not define the way that I see the world. I am a human being, and I'm really not that different from other human beings on the most fundamental levels. The only difference between me and most people is that I don't believe that I am limited by anything. I believe that I can be anything that I want to be and that I can experience anything that I want to experience.