With Livy, we always need to stop and think... his numbers aren't always realistic, and perhaps his description of an event may be a little slanted, but I've never seen any reason to believe he would report complete fiction. (Not including the earliest history of Rome, which was anyone's guess even in Livy's time) The events of the Second Punic War would've been reasonably known to him and to other writers, so the events he described surely happened. Fortunately, in the case of the Punic Wars, Livy probably drew heavily from Polybius' work, which is generally considered among the more scholarly of Roman Historians.
Unfortunately, there is so much lost ancient literature regarding this period. Polybius' entire account of those years is lost, (though likely preserved in part by Livy). The work of Dio Cassius is fragmented, and that period is also mostly lost, and so on and so forth.