The shot won't lead to any changes in the virus, as the virus doesn't "resist" the shot in any way-the virus' surface proteins are either recognized and destroyed by the immune system, or not recognized, in which the virus enters cells within the respiratory tract and hijacks their innards.
Bacteria become resistant to antibiotics in many ways, but often by a process of natural selection in which a population of actively reproducing organisms is exposed to a stress [the antibiotic] which leads to selection of a few organisms that have some resistance. Repeated rapid cycling of subsequent generations leads to bugs that have more and more resistance.
The worst influenza epidemic ever, in 1918-19, occurred way before any vaccines were available.
