Ever tried to think what's above the stars and whole galaxy? Where does it ends?

Whenever I try to think about it, I get an headache. :/

I don't think it does end. It's perfectly reasonable to consider the notion that the Universe is an infinite expanse, therefore having no conceivable end. If that is the case, then there is a lot to even think about, in terms of things we conclude are out there, yet those things will never even be seen door human eyes.

To answer the seconde part of your question, nothing is 'above' our galaxy, so to speak, but around it - I believe the Milky Way is at least linear in some semblance of that meaning, as well as what we know of the Universe. There are various structures throughout the Universe, including intensely hot expanses of gas and particles called quasars, along with remnants of supernovas, hypernovas, other galaxies and nebulae. So, yeah, a lot of stuff.