Your question is an opportunity to revisit this somewhat strange and very shared idea: that "I" is something other than the space of my thoughts. What could be different?
A soul? A soul is a desire for eternity and not an explanation of conscious experience.
Could a thread of thought exist without this supplement of an "I"? Some make this assumption with the 'philosophical zombie', in which mental processes provide no conscious experience. But we don't know a philosophical zombie and even animals with a much smaller nervous system than ours seem to have a conscious experience.
'This' thought and not the other occupies my mind because my neural processes are forming 'this' thought. This explanation is certain, since if an external stimuli were to enter into the process it would instantly give rise to a different thought in my mind.
It remains to be seen whether there is an independent "I" that observes the process. Not. This impression is completely universal and very real, but it is not independent. It is based on two phenomena:
1) One is classic: neural networks observe each other. It is possible to consider one of one's own thoughts, to observe one's mental reflection.
2) The other is harder to grasp: my thoughts are not displaying a computer running a program for a user. I'm following the whole process. I am merging it into an 'exit' called consciousness, which is also a control. The merger is not reducible to its constituents. This is an additional level of information, the level of integration of constituents.
This is the container surrounding the contents. Even in the absence of directed thoughts (mind in the wave), the container is present. The empty set exists, without content.
You can thus understand why you have 'this' thought but also why you feel like something more than it.