Why does anna look for elsa if elsa is pissed off and scared?

They are sisters. That's it. That's the only answer آپ need.

Love.

It's because she thinks that Elsa's the only one who can "stop the winter".

Its because she thinks she can solve the problem

Because, Anna needs to bring Elsa back so that Elsa can stop the eternal winter that she accidentally put over Arendelle.

Anna loves her sister.