I had a similar issue with IE10 when my Avast Free Edition was version 2014.9.0.2007. I then reported to Avast Support via Support ticket and also mentioned it to this forum. After few weeks Avast released version 2014.9.0.2008, after that I installed that update and the issue with Avast Online Security with IE10 causing IE10 to load up it’s homepage really slow was gone and I installed IE11. After that everything came back to normal and working fine.
I don’t use Firefox anymore, only Google Chrome and IE11. I doubt re installing both won’t do any good. I suggest you submit a support ticket to Avast Support and telling them about the issue you are facing with Firefox.