Praise be to Allah.
We ask Allah to accept your repentance.
if what you mean by that physical relationship that occurred between you and that young man was that it involved intercourse, then this is more serious in terms of sin, because intercourse is one of the gravest of things that break the fast, so how about if that intercourse was haraam? This is even more haraam, and what is required in that case is to repent and offer the strictest kind of expiation, which is to free a slave; if that is not possible, then one must fast for two consecutive months; if one is not able to do that, then one must feed sixty poor persons.
If intercourse took place during the day in Ramadan on two or more days, then the expiation is to be repeated the same number of times as the number of days on which intercourse took place, according to the view of most of the scholars (may Allah have mercy on them). This is the view of Maalik, ash-Shaafa‘i and Ahmad. See: al-Mughni (3/33-34). See also the answer to question no. 22960
Based on that, if a person had intercourse on two days in Ramadan – for example – then he must make up the two days on which intercourse took place. He must also, in addition to making up those days, offer expiation. So he should fast for two consecutive months for each day, but he does not have to fast for 120 consecutive days. If he fasts for two consecutive months for the first day, then does not fast for several days, then after that fasts for two consecutive months for the second day, his fast will be valid.
But if that physical relationship that occurred between you involved things less than intercourse, but there was emission of maniy because of it, then the fast was rendered invalid, and in that case it is required only to make up the fast, in addition to repenting; no expiation is required. For more information, please see the answer to question no. 106476
If a woman is required to fast for two consecutive months, then the sequence of fasts is not interrupted by menses; so she should not fast during the days of her menses, then complete the two-month fast after the end of the menses. This has been explained in the answer to question no. 82394
And Allah knows best.