See, I think this is where my confusion on the resolve comes from. Those scenes indicate a built up justification, and then we're told that fell apart because she lost her memories, but then after the opening scenes, it feels like she's built it back up again. I'm pretty sure she even ignores Yon-Roggs orders, literally becoming a rogue soldier. And I don't see how she continues to struggle with proving herself from that point forward. So...
What is her problem?
My problem is that I can kinda see everything being the problem. I do wonder if we're just projecting our own ideas on to the problem element because it simply isn't defined well enough. In-fact, I don't feel like there's really much conflict in her personal throughline. It almost reminds me of the analysis of Captain America: The First Avenger (the story supposedly lacks an intimate personal problem... and basically everything else).
As she learns about her past, it doesn't seem to affect her in any way we can that we can understand, besides her crying once. And Carol trying to prove herself is... it's like it's already resolved in the first ten minutes. People might push her to prove herself ("smile for me?"), but she doesn't. The scenes towards the end cause her to appear as if she Changes, but all I feel is that she's doing the exact same thing she did throughout the entire film. Just blasting people away whenever she gets in trouble. Not listening when others try to control her.
I'd love to see a few examples of how she struggles with Proving herself (or examples of any other problem element) during the middle portion of the film. I think you'll find the only personal struggles to be within those flashbacks/memories, and at the start of the film. Most the rest of it, if anything, is just outside pressure for her to Change/revert.
My thinking right now is that she's either steadfast, or her perspective changes really early on. And she may or may not even have a specific personal problem.