Unfortunately, as a teacher, she's extremely susceptible to this kind of blackmail. Based on the atmosphere shown so far, it seems like this is an Asian country where homosexuality is even less accepted than in Japan (there's still a few of those left), which is already pretty backward about it. In that setting, even that single picture is probably enough to get her fired (or suspended while they investigate and then fired).
She's showing an appropriate amount of terror about this is what I'm saying. It isn't an exaggeration to say that being publicly outed could destroy her life.
Also, just speculation, but it seems like Leni having a string of lovers who broke up with her was no coincidence. Darth Unnie looks to have manipulated her into breakup after breakup via threatening her lovers via blackmail.
Next chapter or two will probably be rough emotionally for both of them. Confronting her mother about this will be super bad most likely, but... there's a chance her mother could be accepting. By no means assured or anything but the previous history we were shown, her mother seems to care greatly about her daughter hitting life milestones. This COULD be because she just wants her daughter to get the most out of life and be happy. Unfortunately, it is much more likely that just like she had generic expectations for her own future, her mother has generic expectations for daughter's future that she expects to be met (i.e. the "I expect grandchildren" mentality).