My second carryon is the size of a laptop bag.

And I should have rephrased it as my pillow is more of a travel pillow, but does not fit in my carry on.

I have taken the pillow separately before, but was not sure if I should just stick my blanket in the same bag as it.

And by the way, this is going to stay in the seat with me. Won't take up anybody's overhead bin space (at least that is what my plan is).