JB. You won't be able to earn her forgiveness. She BD'd you. You are spinning badly. You are heavily into the mindset that there is something that you can do to influence her. You can't do that. You cannot make her forgive you. You cannot make her stop holding onto your past mistakes.
^^^THIS^^^
JB, the doctor thing was a mistake, you owned it, but here's the deal- your W doesn't WANT to forgive you. Not for this, not for all your other wrongs (real or imagined, and believe me she imagines MANY), not for anything. Right now her mindset is "I want JB out of my life and I will cling to anything and everything I can to justify that narrative." ANYTHING you do will be "wrong" in her eyes. Don't tell her you love her? You're cold and indifferent. Tell her you love her? You're too clingy. Don't tell her she looks pretty? You're insensitive. Tell her she looks pretty? You're shallow and superficial.
^^^READ THIS. UNDERSTAND THIS^^^ It is why we tell you to pull back, leave her alone, give her time and space and work on YOURSELF. Because anything you try to do for her is going to fail to impress her.
This is what you are up against. This is also the most difficult concept LBS's struggle to understand, because it makes no sense in the context of a previously happy marriage.