Praise be to Allah.
There are many hadeeths about the virtues of Hajj which indicate that it erases sins and expiates for bad deeds, and the individual returns from it (free of sin) as on the day his mother bore him.
See the answer to question no. 34359
But this virtue and reward does not mean that obligatory duties are waived, whether they are duties owed to Allah, may He be exalted, such as expiations and fulfilment of vows, or duties that he has not yet fulfilled, such as zakaah that he has not paid or fasts that he has to make up, or duties owed to other people, such as debts and the like. Hajj brings forgiveness of sins, but it does not mean that these duties are waived, according to scholarly consensus.
If a person delays making up Ramadan fasts, for example, and that is without an excuse, then he does Hajj and it is accepted, his Hajj brings forgiveness for the sin of delaying, but the obligation to make up those days is not waived.
It says in Kashshaaf al-Qinaa‘ (2/522): ad-Dumayri said: In the saheeh hadeeth it says: “Whoever performs Hajj and does not utter obscenities or commit sin, will emerge from his sins as on the day his mother bore him.” This has to do specifically with sins that are connected to the rights of Allah, may He be exalted, in particular, and not the rights of other people. The duties themselves are not waived. So if a person owes prayer, expiations and other rights of Allah, may He be exalted, they are not waived, because they are duties, not sins; rather the sin is delaying them. So the delay is waived by Hajj, but the duty itself is not. If he delays it after that, the sin is renewed. So an accepted Hajj brings forgiveness for the sin of non-compliance, but does not waive the duties themselves. This was stated in al-Mawaahib. End quote.
Ibn Nujaym (may Allah have mercy on him) said in al-Bahr ar-Raa’iq (2:364), after mentioning the difference of opinion about Hajj being expiation for major sins: To sum up: the matter is controversial and there is no certainty that Hajj expiates major sins involving the rights of Allah, may He be exalted, let alone the rights of people. If we say that it expiates everything, that does not mean, as many people think, that debts are waived thereby. The same applies to making up prayers, fasts and zakaah because no one says that. Rather what is meant is that the sin of delaying payment of the debt is waived, but if after standing in ‘Arafah he delays paying it, he is sinning now. The same applies to delaying prayers until after the time for them has ended. The sin is erased by means of Hajj but the duty to make them up is not waived. Moreover, after standing in ‘Arafah, he is still required to make them up, and if he does not do so, he is now a sinner according to the view of those who say that he should make them up immediately. And the same applies to other actions by analogy. To sum up, no one suggested that the hadeeths which speak of the expiation of sin by virtue of Hajj are general in meaning, as is clear. End quote.
To conclude: you still have to make up the days that you owe of Ramadaan, and your duties cannot be discharged except by doing that.
And Allah knows best.