Usas LES si vas a presentar a la señorita Gómez ante VARIAS personas (plural: LES) Usas LE si vas a presentar a la señorita Gómez ante UNA SOLA persona (singular : LE)

You can say both, but it depends how much people are listening you. If you are talking to one person you say LE. but if you are talking to two or more people you say LES.

The sentence you wrote is perfect, and insteed to what Henry says, the part "que estudió junto conmigo " is perfect, because "junto conmigo" can be used in this case. It's not bad "que estudió conmigo ", because it means the same than the another phrase, but in this case both could be used within your sentence. And about "le" and "les", your sentence uses "les" because you are talking to several people, therefore it's plural, and the plural wya of "le" is adding it a "s", and then it becomes "les". I hope I'd helped you!

"Les voy a presentar a la señorita Gómez que estudió conmigo en una escuela hace varios años"