Praise be to Allah.
Whoever passes the meeqaat without entering ihraam has to go back and enter ihraam from that point. If he got off the plane in Jeddah, then he has to take a car to the meeqaat of the people of Najd and enter ihraam from there. If he enters ihraam from Jeddah and he is intending to do Hajj or ‘Umrah, then he has to offer a sacrifice as expiation for passing the meeqaat (without entering ihraam).
Fataawa al-Shaykh ibn Jibreen
See also similar fatwas in Kitaab Fataawa Islamiyyah, 2/202
You did the right thing by going back to the meeqaat and entering ihraam from there. The fact that you took off the ihraam garments does not mean that you have to offer the sacrifice, because you did not enter ihraam in the first place. Ihraam means the intention to enter the rituals, not just wearing the garments of ihraam. Based on that, what you did was correct and you do not have to offer any kafaarah (expiation), praise be to Allaah.