I've been the same way all my life. What has helped me the most is realizing that self-consciousness is a baseless fear and it shouldn't stop me from trying things. I know that the only way to get better at doing something, is to try it, keep trying, and soon enough I'll do it like everyone else. If people think you suck at it, who cares?
Going back to the dancing, I still think the reason I think I suck at it is that in every physical activity I do, my movements are purposeful and calculated. Thus, thinking doesn't know what movements to make to translate this feeling, so it just ends up feeling awkward and pointless.
But when I feel like dancing, I don't want my movements to be calculated and purposeful. I want the music, the feeling it's generating inside me, to move my body with it, without any thinking involved. I want it to be pure Se. Maybe that's why ESTPs are better dancers, because they are dominant sensors not thinkers?
So I am content doing my own form of moving to music, which mostly involves very subtle grooving movements, where the feeling of the music kind of flows from one end of my body to the other.