What should I do about the false oath I swore to my wife so that I would not leave her, after I repented to Allah and ended my relationship with that woman?

You have done well by repenting from the sinful relationship, and your repentance must be sincere, accompanied by blocking all means that lead to it. Your wife is not permitted to harbor ill suspicions about you based on your past, and it is forbidden for her to spy. You must avoid situations that raise suspicions. The Sharia permits lying to one's wife to preserve the marital relationship, but swearing a false oath is a clear sin unless there is an unavoidable necessity that can only be resolved through it.