Generally speaking, there should be a relatively simple way to test this, at least in a basic way (which won't consider all factors, but it's a start).
Reboot your system, so to eliminate any other potential problems (like resources not being released correctly by some program ran before).
After rebooting, wait at least 10 minutes before running the following test. Be sure Windows (or any program) is not using your bandwith (for example to update something).
Then, while Avast shields are active, test with speedtest. Write down the results (which you should repeat at least 3 times to see the distribution of values).
Now right click on Avast's tray icon and disable all shields. Test again speedtest with the same server (also several times, writing down the results).
Compare the results. This is not going to give you the whole picture, as other things may be conflicting with Avast shields too, and other possible features of Avast may be affecting the results (who knows what the firewall is doing, just to mention an example, using your own logic and suspicions). In addition, your normal browsing is performed all over the world, while speedtest is testing with a specific server (usually the one closer to you geographically, but you could select it too).
So, although it's not a definitive test, and the results may point to a wrong conclusion too, it may be worth to test the difference.
I would even repeat the tests after, say, 30 minutes and without rebooting, writing down all the results, always using the same testing server.
Please post the speedtest results here.
