Bacteria do not become resistant to an antibiotic because they were exposed to it. Resistance appears first as a chance variation in a few individuals, long before any drug arrives. What the drug does is remove the competition. Kill the susceptible bacteria and the resistant few, which were previously a negligible fraction, inherit the whole environment and multiply freely. This is why finishing a prescribed course matters, and why using antibiotics where they can do no good, as with a viral infection, is not merely useless but actively harmful.