@Sahmir I'm pretty sure that was her own inner thoughts. Remember that this is from her perspective, and thus most, if not all, of those thought boxes should be hers. She was calling herself ugly and foolish, lamenting how ignorant she was her entire life. It's not obvious, but he did actually care about her. He just couldn't act on it and reveal everything to her. With how naive she was there was the risk that she might unintentionally reveal that he is a spy while casually talking with one of her family members. To the very end, she never truly knew what it was like outside till her house was burned down. Sure, she knew that the people were poor, but she didn't truly understand why. She was the epitome of sheltered, regardless of how intelligent she might have been.
As for why she was so broken and went with execution, her entire life was destroyed. Her home was burned down with most of her family, she probably witnessed both of her parents die in front of her, and the reality of how luxurious her life was at the expense of others was only just hitting her. The amount of hate suddenly directed at her wasn't much better. Her family may have been horrible people, but she loved them and they loved her. She knew nothing of how horrible they truly were to other people, and they made sure of that by keeping her so sheltered.
All in all, it was too much, and the idea of living the rest of her life in some monastery in the mountains while lamenting everything that happened felt like it would have been horrible and unbearable. She was over it and just wanted it all to end so she could rest eternally. At the very least that way she could reunite with the only people that she believed truly cared about her, namely her now dead family. However, now that she regained her memories, she has come to the (unnecessary) conclusion that she isn't done atoning for the sins of her family. She probably figures that she has no choice but to live with these memories, and thus since death didn't save her she feels she has no choice but to go with option B, the Monastery, while punishing herself all the while.
Both our MCs are heartbroken and either seek death(In Shirley's case before she was reborn) or attempt to close off all emotions in order to survive(As is the case for both Shirley once she realized she can't use death to escape, and Kaid when he was forced to sentence her to death). Both Kaid and Shirley have it hard, only Kaid didn't have to remember what it's like to see his family and home burn to the ground while mistakenly believing that their lover(who is responsible for her family's death btw) never actually loved them, nor does he remember what it's like to have his head cut off. Even if she never gets back together with Kaid, I just hope that Shirley can eventually learn to forgive herself for her ignorance and eventually come to love herself again. The sins of her parents are not hers to bear, nor should they be.