Is what the questioner did – leading the prayers despite not being the eldest – valid, and is his fear during prayer considered showing off?

If your friend is the regular Imam of the mosque, then you made a mistake by stepping forward ahead of him, because the regular Imam has more right to lead the prayer. However, if he is not a regular Imam, and the mosque does not have a regular Imam, and you are the most knowledgeable among those present, then there is no blame upon you for seeking to lead the prayer. The fear of making a mistake in recitation is not showing off. It is advised to avoid stepping forward to lead, due to the pitfalls involved. Indeed, the Companion Sahl ibn Sa'd feared the responsibility of imamate because of the Prophet's (peace be upon him) saying: "The Imam is a guarantor; if he completes [the prayer], it is for him and for them, and if he falls short, it is upon him and not upon them."