Praise be to Allah.
What this person told you is not correct, because Hajj is only obligatory once in a lifetime, because of the hadeeth of Ibn ‘Abbaas, which says that al-Aqra’ ibn Haabis asked the Prophet (peace and blessings of Allaah be upon him): “O Messenger of Allaah, is Hajj (to be done) every year or only once?” He said: “One once, and whoever does more than that, it is a voluntary (act of worship).” Narrated by Abu Dawood, 1721; classed as saheeh by al-Albaani.
Since you did Hajj before that, then you do not have to do Hajj again.
There are three months of Hajj: Shawwaal, Dhu’l-Qi’dah and Dhu’l-Hijjah. Perhaps this person understood from the fact that they are called the months of Hajj that whoever does ‘Umrah during these months is obliged to do Hajj. But this is incorrect, rather the reason why they are called the months of Hajj is that Hajj must happen during these months, not before or after them.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about a man who did Hajj tamattu’, then after doing ‘Umrah he went back to his city and did not do Hajj – does he have to do anything (offer any expiation or ransom)?
He replied: You do not have to do anything, because if a person is doing Hajj tamattu’ and enters ihraam for ‘umrah, then decides not to do Hajj before he enters ihraam for Hajj, then he does not have to offer any expiation or ransom, unless he vowed to do Hajj this year. If he made such a vow then he is obliged to fulfil his vow.
Fataawa Ibn ‘Uthaymeen, 2/679.