The girl I like is in a bad mood and doesn't reply to the news. Should I continue to care about her or stop bothering her? Very tangled ...

When sending messages, don't always ask her why she is unhappy. Tell her something interesting about yourself. You like her, do it silently. You shouldn't let her reply. But you have to believe that just because you are in a bad mood and don't want to reply doesn't mean you won't read it. You are willing to accompany her when she is unhappy, without asking for anything in return, and you will be moved when you think about it later.