Welcome,
The bad guys / gals are getting sneaker with their attempts to infect our computers for their purposes. The fact that you did nothing different doesn't mean that they didn't mess with your targets. The possible unsafe conduct by others on your network should not infect your machine.
If Norton has blocked an attack you might want to clear cache files and temp files so that the only place the 'nasty' might be is locked up inside 360.
Using one of the free, on demand scanners like
http://www.malwarebytes.org/products/malwarebytes_free
or
to get a second opinion about your system health is a wise thing to do. Use only the free version and do not activate the pro or free trail version as they do conflict with 360. There are additional helps if more is needed.
Keep us posted