How can one repent and get rid of the whispers of doubt and spying on one's husband, especially when there is no evidence of his betrayal?

It is not permissible for you to spy on your husband or to harbor ill thoughts about him without justification, for the fundamental principle concerning a Muslim is their integrity, and it is obligatory to think well of Muslims. You must disregard obsessive thoughts and not pay attention to them, and beware of going too far with them. Among the most important things that will help you in this is seeking assistance from Allah and increasing in supplication.