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.
The prohibition of taking boyfriends and girlfriends is proven by evidence in the Quran and Sunnah. We will mention some of them briefly because it is not suitable here to lengthily elaborate on the matter and details can be found in the books of scholars.
Among these pieces of evidence are the following:
1- Allah Says (what means): {[They should be] chaste, neither [of] those who commit unlawful intercourse randomly nor those who take [secret] lovers.} [Quran 4:25]
{…. desiring chastity, not unlawful sexual intercourse or taking [secret] lovers.} [Quran 5:5]
At-Tabari, said in his Tafseer (interpretation of the Quran): “He took her as a girlfriend and she took him as a boyfriend, and he took her for himself as a friend with whom he commits fornication (or adultery).” [End of quote]
2- The story of Marthad Ibn Abu Marthad with ‘Inaaq who was a girlfriend of his in the pre-Islamic Era of Ignorance. When Islam came, it invalidated that, and their story was the reason for the revelation of the verse: {The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers.} [Quran 24:3]
For more details on the story, one may refer to Sunan At-Tirmidhi and to the books of Tafseer (interpretation of the Quran).
There are other pieces of evidence, but it is not the place to lengthily elaborate on them as we have already mentioned. We advise you to sit with the scholars in your country in Islamic Centers and so forth and ask them about the pieces of evidence that you need to know or responses on misconceptions.
Allah Knows best.