Easy way to curve a virtual screen?

So I have a virtual screen in my program, which consists of 13x9 quads that are aligned so that the virtual screen looks contiguous. Every quad is displaying a different texture and the textures can change, that is why I used that many quads instead of a plane. (Can I make this maybe easier?)

How do I make this virtual screen curved? What I want to achieve is that the outer edges of the virtual screen are closer to me, i.e. that the view looks spherical. The reason why I want to do this is because I have this virtual screen attached to my main camera and depending on the camera movement the textures on this virtual screen change. However, moving around with a flat virtual screen makes me dizzy and I want to curve it, to make it look more natural.

I looked into shaders yesterday, but I do not know how to program shaders that can do that. I figured it would be easy vertex manipulation, but unfortunately it is not a trivial task. I looked into vertex manipulation from within my code but I couldn't figure out how to do that either. What do you think the easiest and best way would be for my case?

The program I am making is using Google Cardboard, so I see a flat virtual screen in VR, but moving my head creates a weird visual effect for me, that gives me headaches :). Maybe changing the lens distortion parameters would create this effect for me?

Thanks in advance!