All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The Sunnah is to recite loudly during the prayers one is supposed to recite aloud, and to recite silently where one is supposed to recite silently. Whoever does the contrary, i.e. recites loudly where one is supposed to recite silently and vice-versa, then he contradicted the Sunnah but his prayer is valid.
As regards whether or not he should prostrate for forgetfulness, then the scholars differed in opinion in this regard. However, whoever prostrates for forgetfulness, then he kept himself on the safe side. For more benefit, please refer to Fatwa 90419.
Moreover, the scholars differed in opinion about whoever recites Al-Faatihah silently whereby he should have recited it loudly, and then he remembers while reciting it, whether or not he should start from the beginning or just continue the remaining parts aloud. Some scholars are of the view that he should start from the beginning as long as he did not bow down, and others are of the view that he should just resume. However, since you started from the beginning, then you have acted according to a considerable opinion of the scholars .
Those of the first opinion have no evidence proving that adopting the other opinion invalidates ones prayer. Rather, all things the considered, the second is the more correct opinion.
Allaah Knows best.