iphone continues to redirect on mobile sites

Problem: Everytime I try to connect to any website on my iphone, I think only when the website has a mobile site, I am redirected to ads. This is both on safari and when I google sites and from the FB app. I'm not able to access normal sites like Time.com, huffingtonpost, newyork times. These are not sites that I should have to avoid going to.

Solutions: I don't know why but this is happening to both my phone and my boyfriends. I have the iphone 5C and he has the 5S. It's happened in the past but never for this long (it's now been 10 days). I thought it was because the network has been hacked but even if I use my 3G or another wireless connection it continues. I have tried to block the sites so they don't continue to redirect to others which has worked and now it doesn't take me to the appstore but now when I go to a site like time.com I am redirected once and it says that webpage has been blocked (because I blocked it). If I am fast enough sometimes I can hit the x when the site im going to has partially loaded but this isnt the right solution either. I tried to disable the javascript but that only partially helped. When I go to sites that do not have a mobile site I don't have this problem.

PLEASE HELP ME!