Is a prostration of forgetfulness (sujud al-sahw) obligatory for someone who emits a slight whistle when pronouncing the letter "ra" during prayer, or whose voice involuntarily rises when reciting a small part of a word, knowing that he read words from Ibn ‘Uthaymeen stating that one does not prostrate for unintentional loud recitation in an inappropriate place?

Prostrations of forgetfulness (sujūd as-sahw) are not legislated when you vocalize some letters or part of a word, for the Prophet, peace and blessings be upon him, would sometimes let the Companions hear a verse during a silent prayer. Sujūd as-sahw is also not legislated when one whispers in a place where vocalization is prescribed, especially for someone afflicted with waswasah (obsessive whispering). As for what you mentioned about a whistling sound when pronouncing the letter rā’, this is an effect of waswasah, for whistling is characteristic of the letters ṣād, zāy, and sīn, and does not occur when pronouncing rā’. Therefore, it is advised to fear Allah, perform prayer, and recite away from the influence of waswasah, and do not perform sujūd as-sahw for these reasons.