I’m sorry I hurt you
I think that is brilliant, and the heart of real love. I am NOT suggesting that you should lie – if you are not sorry you hurt, offended, or upset her, don’t say you are sorry (and please get some help!). Thing is, you can be sorry for her feeling bad even if you did nothing wrong. Assuming you don’t enjoy making her feel bad, why wouldn’t you apologise for doing something that caused her to feel bad?
The step beyond this is to consider how you might avoid hurting her in the same way in the future. In some situations it’s not possible, or possible but not reasonable, but many times you can do or say things differently and avoid hurting her. Of course, some will say, “She needs to toughen up – ignoring to her weaknesses is not doing her any favours.” While this is sometimes true, you being the one “toughening her up” is a bad plan. She needs you to be on her side, to be supportive, to be loving and kind. It is far better for you to help her see that she has over reacted to others AFTER you show her some sympathy.