How to say "I can't help but..."
There are actually two meanings of "can't help but" here, with a rather subtle distinction. In your first example, the guy cannot control the fact that he wants to cry - he simply let go of his emotions. In your second example, you can control your behavior, and in fact you're very determined to do it.

In the first example, an equivalent phrase would be: 


  不由自主地 (did something without control)


In the second example, an equivalent phrase would be 


  没有办法不[责怪你]  (have no choice but to [blame you]).  


You're right that the phrase 不由得 is rarely used. In fact, when it is used, it usually has a different meaning: telling another person "You have no choice", e.g.


  这件事情不由得你 = You have no say in this matter