The legal or legalistic phrase for when one is coerced to do something is "under duress":
She signed the agreement under duress.
If you fail to do something, it might be because you were powerless to do it, as suggested above. Powerlessness explains inaction. But if you do take some action, one that harms another for example, it doesn't sound right to say "I did it because I was powerless to do otherwise"-- if inaction was available as a choice, or if the action taken is a clear act of volition.
"The assailant came at me brandishing a knife. I fired my gun. I had no choice."
"You gave me no choice -- you were selling drugs to children and I had to turn you in to the police when you refused to stop."
I don't know of a single adjective that carries the full force of "having only one choice", that is, having no choice at all but rather an obligation. These words nip at the edges: "obliged", "bound", "constrained", "obligated", "compelled".