Your question is a common question about Romeo and Juliet. For your essay, your initial answer is easy. Yes, Romeo and Juliet are really in love. Or no, Romeo and Juliet are not really in love. It's your essay, so you need to pick which ever answer you believe to be true. There is no correct answer. It's all about how you defend your answer. That's the other way to tackle this question. Pick whichever answer is easier to defend.
Personally, I'm a bit of a cynic when it comes to Romeo and Juliet. No, I do not think that they are in love. First, I don't believe that love at first sight exists. Millions of people world wide will disagree with that, but that doesn't change my feeling. Second, I really don't think Romeo is truly in love with Juliet. I think that Romeo is in love with the idea of being in love. It has always bugged me that eight hours (or so) prior to meeting Juliet, Romeo was beside himself because Rosalind didn't love him back. Juliet seems more like a rebound relationship than actual love. For you essay, you could make a case that Romeo is a Petrarchan lover. That's more or less someone who wants to be in love for the sake of being in love. They love the idea of love.
I suppose Juliet might really be in love with Romeo. I don't want to say it's completely not possible. I just don't think it's likely. She's 13 years old. I do not see her being old enough or experienced enough to really know and understand what true love is.