You will most likely need dedicated compositing software unless your NLE has some basic functionality built-in that allows you to do this. Here are some free or low-cost examples of compositing software:
Natron (GPL Open Source)
This should be a comment I guess but I don't have enough rep.
What kind of monitor are you using?
My iPhone records my 27" Retina 5k monitor just fine.
My guess is you have an LCD monitor and you are having polarizing issues (