been a long time coming
I see it has been days since you posted your problem, having suffered like you for weeks with slow internet (until Safari simply stopped working 3 days ago), the problem for me was resolved yesterday.
Although I've used Macs only for a long time, I know almost nothing; searching for an answer was a problem. I have learned more about WiFi, connectivity, and other things I'll forget in a couple of days. It took time to figure out what words to use to enter in the browser to find the answer to my problem.
Having spent 3 days at a neighbor's researching and coming home and trying ALL the suggestions, there was only one of a hundred things I had tried that worked.
I installed Google and switched my browser to Google from Safari. Before doing this, I made certain everything was carefully backed up, junk deleted, downloaded my bookmarks from Safari, etc.
Yesterday I used these two links, did some of what each suggested, but I do think that simply installing Google as my browser fix my problem. Will know better as the days pass, but I am jubilant to be online again.
There is a section on the second link about problems with Safari.
http://osxdaily.com/2014/10/25/fix-wi-fi-problems-os-x-yosemite/
http://fieldguide.gizmodo.com/the-worst-bugs-in-os-x-yosemite-and-how-to-fix-them-1652690924