Learn Spanish (Latin America): Estoy avergonzado por mi error.

We use estar because feeling embarrassed is a temporary emotion. If you want to describe someone who is generally shy or easily embarrassed (a personality trait), you use ser, but the adjective changes to vergonzoso (e.g., soy vergonzoso).

Wait, shouldn't 'embarrassed' be embarazado?

Be careful! Embarazado (or embarazada) is a famous 'false friend' that actually means 'pregnant'. When you want to say you feel embarrassed or ashamed, you always need avergonzado.

Why do we use por here to mean 'about'?

In Spanish, por is often used to show the cause or reason for something. You are embarrassed because of your mistake. Even though we say 'about' in English, Spanish uses por to link the emotion to the thing that caused it.

Does avergonzado change depending on who is speaking?

Yes. Because avergonzado is an adjective describing the speaker, it must match their gender. A male speaker says estoy avergonzado, but a female speaker would say estoy avergonzada.