Ultimately its between you and your doctor. This is somewhat common in AA and it's because people do, very often, start abusing prescription drugs and say they are fine because a doctor gave them to me. I'm wondering if this has been her experience in the past so that is why she is being more forward about it with you?
When I stopped I was on Lorazapam for awhile to help with the shakes and sickness and my sponsor was greatly concerned about me abusing them. I did not abuse them ever but he asked me often if I was still taking them and if I planned to ween off of them. He was right, I did need to get off them and did just that over the course of a few weeks and I'm happy I did. He was just very concerned due to his experience with others who were on similar medications.
Maybe due to my experience I am seeing if different but I see your sponsor as being very concerned about you and doing all she can to make you successful in recovery.
On the other hand, I presume you have been working with your doctor for awhile and as long as you are being COMPLETELY honest with them than they should have you on the right track with your meds. If that is the case than tell your sponsor that your prescription medication is a subject between you and your doctor and you no longer wish to discuss it with her! Nothing wrong with that and if she's good sponsor she will understand and do her best to help you anyway even due to her objection. If she has a big ego and only wants to be right than she will not like that and will not be a good sponsor. Good luck!