Terminal command `screen` will not split windows vertically
I think what you want is to ctrla,shifts (split first), and then ctrla,tab to switch to the new region. Now you can ctrla,c to create a new shell in that new region.
If you want vertical split, be sure to check the version of screen that you're running. According to this Unix SE answer, vertical split is NOT a default feature and needs to be patched in.
The TL;DR of it is: you'll need to download and compile a new screen command with the appropriate patch (or at least a newer version if the patch has been merged into the main project).