Fret buzz on first and second frets

Hello, I have some fret buzz on my first and second frets of my E and A strings. I am trying to fix this myself because I want to learn. I think this means I need to adjust the truss rod, right?

However, the bolt thing to my truss rod looks completely stripped:

I can't really turn it.

Does that mean I need to make a new nut now if I want to get rid of this buzz?