Is one held accountable for swearing by Allah falsely due to embarrassment?

If the oath was uttered unintentionally by the questioner, it is an idle oath (yamin laghw) for which there is no expiation. However, if it was uttered intentionally, then it is a binding oath (yamin mun'aqidah) that necessitates expiation upon breaking it (hanth), and the questioner has indeed broken it.