Is it obligatory to fast two consecutive months as expiation for each of the two days during Ramadan when I masturbated and broke my fast because of it, knowing that I was ignorant of the ruling at first, and I desire certainty?

Masturbation is forbidden. If it occurs in Ramadan (definition), and no object is inserted into the private parts, the fast is not invalidated unless semen is ejaculated. If one doubts whether semen was ejaculated, the default is that the fast is valid, and only a make-up fast is required if one is certain of ejaculation, without expiation. If it involves inserting an object into the private parts, there is a difference of opinion regarding the invalidation of the fast, and the more likely view is that it does not invalidate it. However, out of precaution, it is recommended to make up the fast.