So I'm connected to my WiFi with internet access but I'm also connected to an unidentified network?

I'm worried that I may have installed a virus that cause me to connect to me a system unknowingly, is this true or what's going on here? 

This is not possible to connect to a to two different networks at a time and there is no option in your network card and it might be showing this because of that virus that present in your system.

as you said that installed virus may be your system is infected with virus or trojans or you may have created an another connection or bridge connection is created once check in view all network connections

If your PC is infected then firstly scan with trojan remover and reset the windows policies, Internet policies...etc. and then Install a free antivirus programme, update virus definitions scan the whole computer and while scanning disconnect your PC from the Internet.

Once check how many Ethernet cards are connected to the Internet and through LAN or WIFI and if wifi, lan are connected using Internet to access check which one you are using? then disable the other one.