Hi Ann,
I think you would know from the context but you could always use 13 heures for 1 pm, taking away the confusion.
e.g.
Nous aurons la réponse d'ici une heure. (We'll have the answer within one hour.)
Nous aurons la réponse d'ici treize heures. (We'll have the answer by 1 pm.)
Hope this helps!