I know people have asked similar questions before but I feel my situation is somewhat different. I met a graduate student at a conference and we realized that we had a very similar research idea and decided to turn that idea into a paper. We successfully published the paper. I initially wanted to add my advisor's name but decided it would not be in my place to ask as she was not involved at all and she did not ask to be added, so I submitted the paper without her name. It was not quite apparent to me at that time as she did not express any concerns, but looking back, I think what I did was wrong because my stipend came from one of her grants which was not related to the topic I published on (I paid the publishing costs though). Am I right in thinking that I did something wrong? What is going to be the aftermath of this? I might need her recommendation letters in the future and I have the feeling I have marred my relationship with her.
I think what I did was wrong because my stipend came from one of her grants.
There is no connection between funding and authorship. Providing funding is never sufficient to make someone an author. So you have not done anything wrong for this reason.
What is going to be the aftermath of this?
I cannot predict what your advisor will do. I can say what they should do. If your paper is accepted, your advisor should say this is evidence they trained you so well that you are able to do research independently. This makes you and your advisor both look good.
A good rule for research in general is: Do not keep secrets. If you feel a need to keep a secret, it's probably paranoia.