you mean this happens with no email client (Windows Live Mail , Thunderbird) involved? … well then this is all going on at server level, and that’s not a virus, but an hijacked account issue. Report it to your mail provider and see what they can do. Check your contact list too … for intruders (harvesting the same list actually), and block them if you can.
Avast can only take action if an infection is taking place locally.