So, does the flickering only happen when you use a browser? If so, try another browser, like Firefox.
You also need to first find out if there are any "problematic" files on your machine. One good (and free) virus program is ClamXAv. You can get it from here:
http://www.macupdate.com/app/mac/15850/clamxav
Also, did you completely remove MacKeeper?
Before making any kind of backup, you need to get your system as clean as possible. That is why you should run ClamXAV, and completely get rid of MacKeeper.
Let us know the results of doing that first, and then we can help you regarding a backup. If you do need to start with a backup, that process will be somewhat involved, but dooable. It will involve 1) making sure your external drive is "OK", 2) re-partitioning your external drive, 3) insuring that you have a "pure" version of the OS you are running under, 4) downloading the excellent (and free) backup/cloning software SuperDuper!, 5) using SuperDuper! to make a bootable backup of your current system to the "new" partition on the external drive, and 6) insuring that you have all your third party applications (and any updates to any software) "neatly" contained in folders. That will make it easier when you install all those applications after erasing and formatting your internal drive, and then installing the OS.
It is important that you let us know the exact model of your machine, and also what OS you are using. If you are using Snow Leopard (OS 10.6), you will need the original Snow Leopard DVD (and, of course, a working Super Drive) for this project. If, though, you are using Mavericks (OS 10.9), you should have that on a file, which can be used to install it onto your machine.