Have you tried a different network to see if that also seems to be running slow?
As I don't use Avast, I can't say about their program/updates.
Generally speaking, however, the only time an Anti-virus should affect the speed of a program, is when the program is activated, and even then only if the anti-virus is configured to scan on start-up.
This still should not affect your connection speed.
If you want to try a different free anti-virus, I use
AVG along with
Super Anti-Spyware
