Is the wife considered forbidden to her husband if she does something without his knowledge, after he swore to her that "if she does anything else behind my back, without my knowledge, she will be forbidden to me," knowing that she went to the doctor without his knowledge due to her illness, and can this oath be retracted?

What you did by making your wife forbidden to you for doing something without your knowledge is an act of forbidding your wife, and its ruling depends on your intention. If you intended divorce, it is a divorce. If you intended ẓihār, it is ẓihār. If you intended an oath by Allah, or if you did not intend anything, you are liable for an expiation for an oath (kaffārat yamīn). If you intended divorce, you cannot be released from this oath, and when your wife goes to the doctor without your knowledge, a divorce occurs. You can take her back before her ʿiddah (waiting period) expires, provided this divorce does not complete the three divorces. If you intended ẓihār, then upon the fulfillment of the condition, the expiation for ẓihār becomes incumbent. If you intended an oath by Allah or did not intend anything, you are liable for an expiation for an oath when you break it. It is necessary to be patient during marital problems and to avoid words of divorce and prohibition. It is obligatory for the wife to obey her husband and not to leave without his permission. If she leaves without his permission and without a legitimate Islamic reason, she is considered rebellious (nāshiz).