All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His slave and Messenger.
You did the right thing by cutting off communication with this young man and stopping chatting with him; this act is forbidden and one of the causes of evil and corruption. Having lovers (boyfriends) is one of the evil morals of the pre-Islamic period that Islam deems forbidden, as Allah, The Exalted, Says (what means): {…[They should be] chaste, neither [of] those who commit unlawful intercourse randomly nor those who take [secret] lovers…} [Quran 4:25]
However, merely cutting off communication with this man does not constitute a valid repentance as per the Sharee‘ah until you fulfill all the conditions of repentance; namely, regretting the sin and resolving never to commit it again in the future. You should conceal your faults and not tell your father or others of what you did. It is incumbent on a Muslim to conceal his sins. Abu Hurayrah narrated that the Prophet said: “All my nation are forgiven (for their sins) except those who commit sins openly (or disclose their sins to people). An example of such disclosure is that a person commits a sin at night, and though Allah screened it from people, he comes in the morning, and says, ‘O so-and-so, I did such-and-such (evil) deed last night.’ Though he spent his night screened by his Lord (none knowing about his sin), yet in the morning he removes the screen of Allah from himself!” [Al-Bukhari and Muslim]
There is nothing wrong with you both joining a public group on social media in which everyone can see the posts shared by others, and you should beware of any private chatting between you because it may lead to Fitnah (temptations).
We would like to point out that you should hasten to marriage as much as possible and facilitate it; it is the best advice given to those who are in love, as was authentically reported on the authority of the Prophet : “There is nothing like marriage for two who love one another.” [Ibn Maajah]
Allah Knows best.