Is it obligatory to completely clean the inside of the navel by inserting a finger to reach its end with every ghusl?

What you did by over-washing the inside of your navel until you felt pain is not permissible and is an extremism in religion. This is due to the influence of the waswasa (whispers/obsessive thoughts) that you suffer from. In the future, it is sufficient for you, when performing ghusl (definition) (ritual bath) from janabah (definition) (state of ritual impurity), to convey water into the navel while inserting a finger to the end of the navel, without exaggeration. Al-Kasanī al-Ḥanafī, in Badāʾiʿ al-Ṣanāʾiʿ, stated the obligation of conveying water into the navel, and that a finger should be inserted into it for thoroughness. Likewise, al-Nawawī, in al-Majmūʿ, mentioned the obligation of conveying water to the folds of the body, the inside of the navel, the inner parts of the ears, the armpits, and other areas. Therefore, we advise you to turn away from these waswasa. Your ghusl is valid, and you do not need to repeat it.