Praise be to Allah.
If customs and traditions are contrary to Islam, it is not permissible to follow them. That includes preventing a younger daughter from getting married until the older daughter is married, because that is unfair to the younger daughter, in addition to what may result from that of problems and corruption, as the Prophet (blessings and peace of Allah be upon him) said: “If there comes to you one whose religious commitment and attitude pleases you, then marry [your female relative who is under your care] to him, for if you do not do that, there will be tribulation on earth and much corruption.” Narrated by Ibn Maajah, 1967; classed as saheeh by Shaykh al-Albaani in Saheeh Sunan Ibn Maajah.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: It is not permissible for the father or anyone else to prevent the one over whom Allah has given him guardianship from accepting the proposal of one who proposes to her, if he is acceptable on terms of religious commitment and character, on the grounds that he will not arrange the marriage of the younger daughter before the older. This argument will be to no avail before Allah, may He be glorified and exalted, because Allah says (interpretation of the meaning): “O you who believe! Betray not Allah and His Messenger, nor betray knowingly your Amanat (things entrusted to you, and all the duties which Allah has ordained for you)” [al-Anfaal 8:27]. And the Prophet (blessings and peace of Allah be upon him) said: “If there comes to you one whose religious commitment and attitude pleases you, then marry [your female relative who is under your care] to him, for if you do not do that, there will be tribulation on earth and much corruption.”
End quote from Fataawa Noor ‘ala ad-Darb
Shaykh Saalih al-Fawzaan (may Allah preserve him) was asked: Is it obligatory for the father to refuse to arrange a marriage for the younger daughter until the older daughter is married?
It is not permissible for the father to refuse to arrange a marriage for the younger daughter, if she receives a proposal, on the grounds that he has to arrange a marriage for the older daughter before that. Rather this is one of the customs of the common folk for which there is no basis in Islam, which is because they think that it is harmful for the older daughter. If that is true, it is also harmful for the younger daughter, and two wrongs don’t make a right.
End quote from al-Muntaqa min Fataawa ash-Shaykh Saalih al-Fawzaan, 3/152
What guardians should do is not let these customs form a barrier to achieving the aims of sharee‘ah. If you can work something out with your family concerning this matter, that will be good. Otherwise, ask some sincere religiously-committed and trustworthy people to intervene.
Whatever the case, it is not permissible for you to continue in this relationship with a man who is not your mahram. Rather he should either do a legitimate shar‘i marriage contract with you, with the approval of your guardian, even if consummation is delayed until your sister gets married, or you should cut off all communication between you until the decree of Allah comes to pass.
As for remaining in contact, this is something reprehensible, and the negative consequences to which it may lead and obvious to anyone with common sense and religious commitment; how many calamities and great troubles have resulted from such things.
And Allah knows best.