If I am understanding this right you are connecting with the USB WiFi connected to the computer to your phones WiFi, If that is the case then when you are connected to the phones WiFi and the Internet connection is working properly open up Network connections by pressing the
Then type or paste this into the Run Command Box
You should end up with something that looks the pic below, Right click on your WiFi adapter and select properties.
I hope the below pic explains it properly
You might want to do this first
You only said your router was a Linksys router so I am going to guess that the default IP of your router's Lan port is either 192.168.0.1 or 192.168.1.1
You are going to have to change a few settings on your router because by default (ICS (Internet connection sharing)) will give your network a 192.168.137.1-254 IP. It will handle the DHCP for that subnet
Before you follow my advice above you should change your router's setting's, Because when your subnet changes from 192.168.x.x to 192.168.137.x the 192.168.x.x will unreachable
Turn off DHCP for the lan or set it to something high like 192.168.137.180 - 192.168.137.253
IP = 192.168.137.11
Subnet = 255.255.255.0
Gateway = 192.168.137.1
Sorry for taking so long to answer but when I stared answering stuff happened then I fell asleep then I pressed submit reply so if there is some mistakes I should be able to figure it out
made this pic just in case i'm wrong save this Pic to your computer and use Window's paint to say how you connection is .
If you use this method make sure you say what is connecting to what.
LAN = Blue
USB = Yellow
WiFi = A big lightning strike ( or squiggle lines your choice)
What connects to the net = Green