In a nutshell, it's a really bad idea to use two resident AV's together (in this case Norton and AVG.) They are likely to conflict. The confliction might be serious, as in locking your computer when a virus is found, or it may be barely noticeable. Either way, with the AV's competing there will be a performance hit, and it is likely your protection level will be inferior than if you just have one installed.
If you do get an infection, it is likely to be more difficult to fix.
I recommend uninstalling one of the AV's, and using the appropriate removal tool after uninstalling. It may be necessary to re-install the AV you choose to use afterward.
Norton Removal Tool.Choose relevant AVG remover. (for most users it will be the top one on the page. 32bit.)
If your system is infested, I'd also recommend downloading
MBAM, installing it, updating it, and run a full scan.
There are quite a few steps to successful malware removal, more may be required and/or advised, depending on what your situation is.