Antibiotic resistance is one of the biggest up-and-coming problems for humanity, but this case probably isn't the start of the apocalypse.
For one, the woman who died was 70+ years old, lived in India, and had health problems. She was probably immunocompromised, which might be why she died after antibiotics failed. All of you, on the other hand, are spry young teenagers who are less likely to die from a bacterial infection, antibiotics or not.
Stories like these are really bad news for hospitals, but I doubt there's cause to buy a fallout shelter right now. Unless, like, you want to, or something.