I've got a virus sending spam emails off my account?

Hi, I think I've got some sort of virus which got into my email account and started sending everybody in my contacts spam. It sent my dad and two of my male teachers "try viagra" ads (those were three EXTREMELY awkward conversations), but most people got virus links. It's also not sending just one, one of my teacher reports getting 4 in 24 hours. It's not hacked because I changed my password and it's still doing it. My antivirus expired about two weeks ago and I plan to get it renewed but I never got the time. Should reinstalling my antivirus and doing a scan fix the problem? Is there an easier way to do this? Also I heard that there is a microsoft website which will scan your computer for viruses online (no download required). Can someone link me please? Thanks a lot.