Is this intention considered a vow, knowing that the questioner did not intend it to be a vow, and if it is not a vow, does she owe an expiation for breaking an oath?

A vow (Nadhir) is not constituted by mere intention. Rather, it requires an utterance that indicates commitment. If the vow is conditional, then it is not obligatory to fulfill it unless the condition upon which it was made has materialized. And that has not occurred in the case mentioned.