No, you dont have a virus at all.
are you using your AppleTV remote, it can make your Itunes start up when you think youre giving commands to the AppleTV
Even if that isnt the case, that is no indication of a virus and currently there ARE NO VIRUS out there currently infecting Macs.
Nobody that owns a Mac needs to buy anti-virus software. The only recommended malware / checker recommended often here on this board is free.
See also on ITUNES playing on its own:
You are not infected, but you obviously have something configured to play the song. May likely be a third-party application you've downloaded and installed.
Helpful Links Regarding Malware Protection
An excellent link to read is Tom Reed's Mac Malware Guide.
Also, visit The XLab FAQs and read Detecting and avoiding malware and spyware.
See these Apple articles:
If you require anti-virus protection I recommend using ClamXav.