Both would be a problem if they both happened, but they don't. Antibiotics aren't like narcotics, they don't work by having a direct effect on the person or animal taking them, they target the microbe. So, you can't build up a tolerance to antibiotics like you can to painkillers or something. We get most of our antibiotics from funguses, like Penicillin from moldy bread because bacteria and fungi have been locked in evolutionary warfare for millions of years. They compete for resources and try to kill each other off by secreting various chemicals. The weak ones die, but the survivors are able to share DNA, and they develop methods of resisting the last method their enemy used. What happens in antibiotic resistance is that we use an antibiotic, but we use less than it takes to actually kill the bacteria. The ones that survived are able to share that resistance with all the others, and the next time you use that same antibiotic it won't affect the bacteria that have resistance. This is a problem when people get a prescription from their doctor and they stop taking it when they start to feel better, or when they take antibiotics for a viral infection. (Viruses can't be killed by antibiotics.) The huge problem that no one seems willing to confront though, is antibiotics in agriculture. Most antibiotics are used in subtherapeutic doses to increase weight gain, so, all of the salmonellas, e. coli, and everything else you can think of is swimming in low level antibiotic soup all day long, just passing around resistance to it like they were trading Pokemon cards or something. Then if a human gets sick from that bacteria it can't be killed with any related antibiotics. So we end up throwing hugely dangerous antibiotics at it like Vancomycin. Here's a decent paper on it. Some of the better ones are only accessible if you have privileges with a medical research library.
http://www.aphis.usda.gov/animal_health/emergingissues/downloads/antiresist2007update.pdf
