What is a soul anyway? What does it do?
You need to answer these question before you can answer "what does missing a soul do to me", as far as I'm concerned.
I personally like the idea that missing a soul somehow detaches you and prevents from "connecting" with other beings and the world around you. Giving you a jarring sense of "wrongness" deep in your being, a sense that you are at all times alone, wrong.
I'm also very fond of the idea that having no soul makes room for something else to occupy that space and that even if that something is something horrible, having it will alleviate the sense of wrongness you suffer from.