Hey there collin!
Sorry to hear you are having difficulty getting all the functionality from your device that you wish to have.
First things first...
Root access allows for deeper access inside the OS, namely the system files which are not normally accessible. It also allows for things such as tethering, though not all tethering requires root, such as certain wired tethering solutions.
Secondly, TWRP and CWM are recovery programs that are a user accessible backup and flash tool. Standard or "stock" recovery is the built in version of the tool, initiated and accessed by things such as a carrier update to your phone's OS or when you perform a factory reset from within the settings menu on your device.
So...why the background? I wanted to distinguish two terms you may have lumped together, which is easy to do. I know I did back in the day when I was in need of help. Glad you are asking for help.
Moving on now...
Root will give your device the ability to access and use WiFi tethering, whether built-in or by third party app. Not all apps work and this sounds like your problem. The app you are using quite possibly doesn't work or is not configured correctly.
One easy solution...flash a custom ROM (May I suggest Jelly Belly?) which has WiFi tethering built-into it and the problem is essentially solved. That said, let me ask a question or two or three...
...Does the above info make sense?
Do you know how to operate/navigate your custom TWRP recovery?
Do you know how to perform a proper installation of a ROM and Google Apps (GApps)?
Get back to me so I can continue to assist you.
jmar