what was the name of the logical fallacy where you research things that only agree with your beliefs and ignore the articles that do not?

That's not a logical fallacy.

That's simply a type of confirmation bias.

Confirmation bias is not a logical fallacy (so many people on R&S use that phrase but don't seem to understand what it means).

Confirmation bias 

It is, as has already been said, confirmation bias, but here's another aspect of the same thing: the Latin phrase, Argumentum ad Ignorantiam: (appeal to ignorance) the fallacy that a proposition is true simply on the basis that it has not been proved false or that it is false simply because it has not been proved true.

Also, John Kenneth Galbraith observed: "Faced with having to change our views or prove that there is no need to do so, most of us immediately get busy on the proof." Anais Nin said, "We don’t see things as they are. We see them as we are." And Georg Christoph Lichtenberg (1742-1799) said, "With most men, unbelief in one thing springs from blind belief in another."

However, the Christian C.S. Lewis said, "If you look for truth, you may find comfort in the end; if you look for comfort you will not get either comfort or truth only soft soap and wishful thinking to begin, and in the end, despair."  Most people who refuse to examine conflicting evidence are looking for comfort.

Confirmation bias, creationists base their rubbish on it all the time.

Progressive liberalism.

Confirmation bias, evolutionists do it all the time

Confirmation bias.