No it's not a browser issue for some reason a lot of people (including me) are getting this issue. I think it is an issue with there recent update of the website and it is as if they block your IP (I have tried 3 comps and it still doesn't work, even on all browser I could find). To make it work take out the www. from www.starcraft2.com and it should work.
I've been using both claritin and fexofenadine or something like that recently alternately and that's been kinda working, I don't feel like my face is going to explode at least. Eyes are still itchy as fuck though