I had the same problem, which is partly caused by
responding to random spam, clicking on links in spam, and,
ironically, trying to be removed from spam lists. I
finally had to kill several email boxes and start over
with new ones. Now I use specific emails for online
shopping, email lists, etc., and never use my main email
addresses for anything but chosen personal and business
contacts. That will make it easier to terminate and redo
the more vulnerable boxes if it becomes necessary. I still
get some spam there, but not nearly that much, and I NEVER
respond to any of it, or click on any "remove me" links.
I also use Norton Internet Security (Symantec) which does
a fair job of removing much of the spam that does get
through (maybe about two thirds). Probably worth trying,
and, depending on where you are, you can likely buy it at
a discount at Fry's or Costco.
Good luck.