I backed up to my external hard drive about 10 days ago. If I back up now will the virus be transferred into the external drive.
Well, there is a chance your computer may not be infected, Esspecially since you said you haven't logged into it in a long time... which means they would have had to get access to your account with another means.
Something similar happened to me, my old yahoo email that I haven't logged into in over 2 years started sending my main email scam. I put a stop to it real quick by changing my password.
Im my situation my virus or other security threat being on my computer was not the cause.
(alot of scammers will hack smaller sites that dont require a lot of security and they try to use the emails and passwords they get on a lot of email sites and other important things. Sadly, this works a lot because a most people use the same email and password for everything.)
TO BE SAFE:
Back up all your data and download the free version of Malwarebytes from Cnet or something like that and then scan the entire drive.
Then restart your computer in safe mode with networking, and run the same program but scan the computer this time.
Malwarebytes is the same program that most of those bigbox stores use for their virus removal service.
ALSO: Make sure you have an antivirus program... malwarebytes is good but the free version doesnt have much in the way of real time protection with firewalls and whatnot
the best of luck to ya!