Make a list of all the possibilities you can think of. How have you seen secrets being revealed in books, movies, or real life? This could be anything ranging from one of the characters confiding in a friend (and misjudging the friend's ability to keep it to themselves) to the couple being literally caught in the act. At this point, it doesn't matter how believable or even cliché these ideas are. You just need a lot of them.
Go ahead and cut the ones you don't want to write, not because "it's been done before" (you might be able to salvage that) but because it's not how you want the plot/characters to develop. (For example, you may not want to deal with a "sex tape" making the rounds, or a dying parent they could ask for forgiveness and their blessing.)
When you've got a few ideas, play around with the details a bit to add even more options. What if instead of the girl's twin brother, it's the boy's little sister who walks into them kissing? What if instead of a love letter being discovered, it's a letter containing a hurtful joke about the friend crushing on the boy? What if instead of confiding to a friend, one of the characters accidentally lets something slip? What if instead of a extremely public situation, it's just their closest friends who find out? What if instead of the witness immediately concluding that they're secretly dating, they come up with some other explanation? Also, can you combine some ideas? Can you make them even more ridiculous/dramatic/tragic?
Make a plausibility check, and try to come up with explanations for any inconsistencies: If they're usually so careful, what went wrong this time? For some of the options, that might be really hard.
(This is my favourite part of this exercise. It's amazing, really, what kind of "plot holes" can be explained by characters having surprising flaws and weaknesses that can then be fed back into the rest of the story. Whenever my initial reaction was, "But X would never do that!", I've always managed to come up with an explanation that added depth to the character and made the story more interesting.)
Next, for each option on your list, consider your characters. How would they react to such a situation right in the moment? How when they're had more time to process it? While it makes sense to focus on the main characters, make sure to also think how everyone present (or who hears about the incident) would respond. Are the characters reacting with embarrassment or fervent denial? Will they burst into tears, run away, laugh it off, or pretend nothing happened? How do these reactions affect the rest of the scene?
Finally, imagine each possible scene as part of your story. For each option you've written down, check whether the situation itself as well as the outcome fits the tone of your story and the general direction of the plot. Would you rather have a moment of relief when they realize (once they've overcome their initial embarrassment) that their relationship isn't as big of a deal as they feared, or do you want to crank up the tension? Should the couple get closer as a result of their relationship being revealed, or would it work better if they had a fight or even (temporarily) broke up? It really depends on the story.
Cut the ones that you don't want to write, that don't fit the story, or any other reason. Try to flesh out the remaining ones some more, and then pick the one that would work best for the story.