There seem to be a few things going on here, that seem to be getting mixed together, but are actually a bit separated.
1) The trauma occurs, and the MC seems to subconsciously activate magic to protect himself from the trauma. (While it wasn't directly stated that it was magic, yet, but in a world of magic, an ability like that which would otherwise seem impossible, is best ascribed to magic.) This is mainly seen by a type of miasma/aura (I like "miasma" since it often reflects something poisonous) that repels/sickens any woman. (It may also have magically locked away the memory, as a further defensive measure, which could be an explanation for the issue that
@icekatze raised). Since most people in the kingdom do not have magical abilities, this would affect almost all of the women. (This fact doesn't reduce the chances of the Prince having magical abilities, as the main characters in settings with magic existing but being rare almost always end up having magic.)
2) The MC is unaffected by the miasma, allowing her to get close to the Prince. (This is probably due to some sort of magical resistance that she was born with or acquired.) Her interactions with the Prince, and the respect and decency that she continues to show him, helps heal his heart from the (still buried) trauma he experienced.
3) Her being able to interact with him, both only touching him in respectful ways, and without becoming ill herself, helps his subconscious to start to process things in a way that reduces the defensive barrier that it had raised. This, in turn, is why he has been able to interact with other women more, without repelling them. We also see that she initially had to be close by, to protect him directly, but the more he interacted with her and others that weren't harming him, the more it was reduced.
4) Her suddenly disappearing for several days, and him not knowing why, caused his anxiety to flare up, which in turn made the miasma return to at least the same strength it had, initially, until he was able to start interacting with her again. He then is healing again. If the memories of the trauma were locked away by subconscious magic, then her continual healing presence may have weakened that seal, as for him to fully heal, he would need to be able to process and come to terms with his memory, consciously.
5) She asks in this chapter, "I'm a 'woman' as well, but are you truly at ease with me?" after he has recovered the repressed memories. She may have meant this as a question about why she wasn't affected by the miasma, but she is asking in the present time about this, so the Prince seems to interpret it as meaning, "Now that you've recovered your memories, aren't you worried that I might try to assault you, like you've worried other women will?" So he responds to try to tell her she isn't "just some woman" because he knows her character, that he can trust her completely (evidenced by him sharing his most intimate secret with her), and he loves her (how she doesn't realize that he chooses: "My beloved fiance" because he actually loves her has been annoying), but says it in a way that could also be misconstrued the way we have seen.
I also saw a few people commenting about him not noticing he had hurt her, but he immediately senses something is wrong, asks if she is unwell, and thinks he has done something to hurt her, but doesn't know what. He probably thought his comment would be reassuring to her, because to him it was a way to convey that he felt completely at ease around her, and he hasn't really had a lot of experience interacting with women, especially romantically, to know what not to say (though I'm sure if she ever told him she didn't see him as a man, he would realize how hurtful what he'd just said was).
