Am I required to offer a sacrifice (dam) after performing Umrah, having forgotten to make the intention of Ihram from the miqat, knowing that I made the intention upon arriving at Jeddah airport?

Ihram (definition) is the intention to enter the ritual, and its place is the heart. Uttering it with the tongue is not a condition. So, whoever did not intend to enter the ritual with their heart until they passed the Miqat (definition), must sacrifice a sheep in Mecca and distribute it among the poor of the Haram (definition), because entering into Ihram from the Miqat is obligatory, and whoever abandons it is liable for a compensatory sacrifice (dam). As for merely abandoning the verbal utterance while the intention is present in the heart, there is no penalty.