Is what happened considered a binding vow necessitating the continuous fasting of an entire month, or is it a vow of contention for which an expiation for an oath suffices?

Masturbation is forbidden by Islamic law, detestable by nature, and has health detriments. One must repent from it. The vow you made to prevent yourself from it is a vow of obstinacy or anger, and its maker has the choice between fulfilling it or offering an expiation for an oath. Viewing provocative images is forbidden, and touching the private parts for this purpose is indeed masturbation. If you are unsure whether the discharge is mani (spermatic fluid) or madhy (pre-seminal fluid), you have the choice between considering it mani and performing ghusl (ritual bath), or madhy and washing it off.