The problem isn't that humans are becoming immune to antibiotics, the problem is that the things you wish to kill are.
When those (bacteria) are immune, it doesn't matter if you have never used antibiotics: it matters that the bacteria do not care about them.
The problem with overuse of antibiotics is (in short) that you kill off all the bacteria that can't handle it and the ones that can are getting all the food and space: example is MSRA: Methicillin-resistant Staphylococcus aureus, so it is resistant to Methicillin (an antibiotic). Which is bad for you as it will not respond to that medicin. This will be a problem regardless of your history with the drug.
This is the big problem: overuse of antibiotics is not as big an issue for the individual as it is for the group, and so it's hard to put a stop to it.
The information about this topic is easy to find, but to add some references: