Do i have a trojan horse?

So randomly 'My computer' opens about after 3-4 hours on my pc. It opens at least 10-11 times. Then just now the weirdest thing happened. I was playing minecraft. Then the my computer thing happened and when i right clicked on the group i pressed close group. The group finally closed and the close group option came up again. I pressed it and immediately it froze. Then after a while it closed all programs then my mouse turned into an hourglass and i couldn't click on anything. Then it came up with the windows shut down options (restart, shutdown etc) and i press cancel. This occurred after my pc prompted me to search for updates and it downloaded delta. Because i have Norton premier edition i pressed remove file because isn't the updates for xp stopped?

I have windows XP and i have FULL norton 360 premier edition.

Added (1). but i do have AV and also scanned it with NPE. Does this mean i have a rootkit virus or something serious

Install Optimo AV on your computer and run a full scan on your computer. Your computer will surely get free from these viruses and malware that are affecting your computer.

Install antivirus and scan your computer

It downloaded delta - delta = Pup (potentially unwanted program)

run free:

http://www.bleepingcomputer.com/download/adwcleaner/
http://www.bleepingcomputer.com/download/junkware-removal-tool/
https://www.malwarebytes.org/

now tell us what problems your having, if any.