Do I buy one more PSE license?

No.  Just install it. You can install PSE onto two computers, but can only use the program on one computer at a time.    That also means you didn't need to purchase 3 licenses.   For me:   If I were installing on 3 different computers that will be in three different locations (for example:  One computer at home, another computer for one of  your kids at a college 2,000 miles away, and a third computer that MeeMaw has down in Lake Havasu Arizona) I would probably  go the route of buying a new license for each--just to keep things simple. 

If you bought an "Upgrade" (which I don't think is the case here) the license of the  new version is tied to the previous version-Quite literally any previous version of Photoshop Elements, just leave that old version alone- install the new version and you will probably be asked about the serial number from the previous version.  

Your serial numbers are all found inside you adobe account info. 

Is this an upgrade for $79. or a new license for $99.?