Did Loras stay in King's Landing after he was knighted or did he go back to Highgarden?
There is no explicit information regarding this.
Loras squired for Renly Baratheon so in all probability it was Renly who knighted him. Since Renly stayed at King's Landing to serve as his brother's Master of Laws, it is reasonable to argue that Loras must have lived there as well given the custom that squires stay with their masters.
But we don't have any dates regarding this. We don't know when Loras was knighted exactly (We do know however that he was knighted when he was 15, given that he was born in 282 AC, that would make the year either 297 AC or early 298 AC) and when Renly was named to the small council. And therefore we cannot make any educated guess as to whether he kept living in King's Landing even after receiving his Knighthood or if he returned to Highgarden.
We do know that squires occasionally visit their homes during the service e.g. Jaime sometimes visited Casterly Rock while serving as Lord Sumner Crakehall's squire. King Aegon V also occasionally visited Summerhall while he was squiring for Ser Duncan the Tall.
But in Jaime's case, we do know that even though he was close to Lord Sumner, he returned to Casterly Rock once he was knighted. So we can assume, by precedence, Loras must have returned to Highgarden (Even if it was a brief visit) following his knighthood. At least the custom appears to decree so. But on the other hand, Loras and Renly were engaged in a conspiracy to have Robert set Cersei aside and wed Margaery Tyrell instead. It is possible that Loras may have stayed in KL to prepare the ground for his sister's possible marriage to the King. Or that he may have entrusted Renly with that task and gone to High Garden to persuade his family. Varys used the words "Knight of flowers urged his father to send his sister to King's landing", now whether he urged his father personally or in letter, we do not know.