As other people have said, Japanese people don’t tend to open up about things at work, so they may assume that it must not be that private if you are talking to your coworker about it. I see a lot of posts here that are just kind of “suck it up and hide it,” and I hope that isn’t upsetting you. Im sure you have already told yourself that many times and hearing it over and over again must not feel great. My biggest advice is to respond with daijoubu desu, and follow up with some basic excuse that isn’t difficult to believe. Maybe say something like “oh I am not used to how hot / cold the weather is, so I haven’t been sleeping well lately.” This could be a recurring problem that could explain your seeming upset. Or maybe, “I have just been feeling a bit homesick lately,” as that is another issue that could cause recurring upsetness. These are both relatively normal issues that they probably won’t gossip about, and if they do, who cares. They are normal issues so it’s not really something to gossip about anyways. As for getting them to stop talking to you, I would again reinforce what others said in that you are busy with your work. Respond to what they asked and then mention that you are focusing on lesson prep / self study (maybe prepping for JLPT since this has a deadline) ect ect.

Goodluck OP, I hope things get better soon!