Issue with secure websites

I am having problems visiting sites that are secured (https). I'm not sure when, but lots of websites have changed to https, including google's search engine.

When I am browsing on my phone, I can access http://www.bing.com, but not https://www.google.com. I also cannot access startpage or any other search engine that uses google's results. As a third example, I can visit http://www.amazon.com but when I try to sign in to my account, I cannot because it is https://www.amazon.com.

I have looked for a solution, but only found answers for DNS issues on desktops. It may be a similar issue, but I haven't come across anything that makes sense to me. Part of the problem finding a solution is apples help forum is also https. On top of that, searching for https in help forums returns every single forum post because they all start with https.

Here's one final thing that adds some confusion: as soon as I log on to any wifi source, I can visit all the https pages I want. So it is only blocking secure web pages on mobile data.

I have no clue about this. Any help is greatly appreciated. (Although, I am absolutely NOT INTERESTED in upgrading to iOS 7)

Thanks in advance

Iphone 3GS, iOS 6.1.3, browsers tried: safari and dolphin. Carrier: GoSmart by T-Mobile.

 

Thanks. I'm not sure if that applies to me since I am not using iOS 7 or OSX 10.9. It doesn't appear iOS7 is even available for the 3GS.

I will visit the gotofail site and see what happens.

Update: I can not load https://www.gotofail.com/ or ANY https web page.

 

No that didn't help.

About the ssl flaw- it seems such a flaw would make navigating secure sites more dangerous, but not stop me from doing it. Am I incorrect?

 

My time and date are set to automatic updates.

I don't know anybody or have access to another phone on my carrier. It is gosmart by t-mobile, and uses t-mobiles apn settings for data.

I will be calling them today.