Well, it is not even certain that the switch the PC is connected to knows the IP address of the PC. If it does, you would need to query the respective tables where it is stored. That might be the ctAliasTable of Extreme switches, or something else. But after a link-down event relevant information is lost from the switch, e.g. the MAC address(es) seen on the port while it was up. Thus the switch might never have had the information (IP address), and it might have already forgotten the information (MAC address) you can use to find the IP on the router.
Anyway, you still to somehow react to receiving the trap and then start looking for additional information.
A good way to get all the information about an end-system that was connected to a switch port that went down would be via ExtremeControl, which can be deployed in a visibility only mode (using optional MAC based authentication).
Sorry that I cannot give you a simple solution with just Extreme Managament Console (XMC).
I'm trying desperately a way to create a "Flex view" using Extreme managment console but I can not understand what it is the field to add in the flex view that can show me the ip address of the pc besides the message information of the alarm.