All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
What appears from your words is that you actually made the intention at the Meeqat before going beyond it. The Ghusl that you made after arriving at the Meeqat and your pronouncement of the Talbiyah indicate your intention to perform ‘Umrah. An intention does not need any effort nor requires to be pronounced, as it is a heart-based act. One only needs to intend to start doing the act of worship. What is apparent to us is that you intended to start the rituals of ‘Umrah, as you said, "Labbayk Allaahumma! ‘Umrah." If this is the case, then do not pay attention to these whispers. However, if you are sure that all the acts that you did, including the Ghusl and Talbiyah were lacking the intention of ‘Umrah and that you did not make the intention except after going five minutes past the Meeqat, then you have passed the Meeqat while you were not in a state of Ihram. In such case, you should have returned to the Meeqat to assume Ihram there. If you did not do so and assumed ihram at the place where you were, then you would be required to offer a sacrifice; which is one sheep, to be slaughtered in the Sacred Precincts and distributed among the poor there. You may authorize someone else to do this on your behalf.
Allaah Knows best.