Is my prayer valid after I prostrated once at the end of the prayer to compensate for a missed prostration, then repeated the two prostrations and the sitting between them, then prostrated before and after the salaam?

If a worshipper doubts the number of prostrations (sujud (definition)), they are required to immediately perform a prostration as long as it is possible to catch up, because doubting a deficiency is like certainty of it.

If performing the prostration is delayed until the end of the prayer, then the matter has details: - If the doubted prostration was from a rak'ah other than the last one, then it is too late to catch up, and it is obligatory to perform a rak'ah in place of the deficient rak'ah. If the worshipper does not do so, their prayer is invalid and must be repeated. - If the prostration was from the last rak'ah, it is sufficient to perform one prostration and then repeat the tashahhud (definition) because it occurred out of its proper place. If the worshipper performs two prostrations with a sitting between them and repeats the tashahhud, their prayer is valid. However, if they do not repeat the tashahhud, their prayer is invalid according to some scholars.

In the case of a valid prayer, the prostration of forgetfulness (sujud al-sahw) here is recommended to be after the salam, because it is a prostration for an addition. The prayer is not invalidated by an additional prostration of forgetfulness due to ignorance.