Is what the questioner said considered a vow: "O Lord, if such and such happens, I swear by Allah that I will be constant in prayer"? And is he sinful for abandoning prayer to get rid of whispers, and what should he do now?

What you did by abandoning prayer is a greater sin than breaking your conditional oath. Abandoning prayer is one of the greatest sins, and it is not permissible for a Muslim to abandon prayer due to waswasa (whispers from Satan). Rather, you should ignore these whispers and pray like everyone else. You must repent to Allah for abandoning prayers. Since you swore an oath to maintain prayer upon a certain condition occurring, and then broke your oath, you are obligated to perform an expiation for the oath. This expiation is: feeding ten poor persons, or clothing them, or freeing a slave. If you are unable to do any of these, then you must fast for three days. This is if you verbally uttered the oath with your tongue. If it was merely an intention, then there is nothing upon you.