Is it valid to perform the prostration of forgetfulness (sujud al-sahw) after observing the Sunnah prayer that follows the the obligatory prayer, and then recalling the prostration of forgetfulness after having performed the Sunnah prayer?

Prostrations of forgetfulness (Sujud Al-Sahw) after every prayer are not legislated. Their legislation is only for rectifying deficiencies in prayer due to an increase, decrease, or doubt.

If Sujud Al-Sahw is legislated and the worshipper forgets it, then if a long time has passed, it is dropped; otherwise, he should perform it.

The cure for obsessive whispers (Waswas) is to disregard them and pay no attention to them. The one afflicted by Waswas should not heed the whispers and should not perform Sujud Al-Sahw.