Most philosophers, me included, would say that we do not choose to feel what we do. Ever since the ancient Greeks, emotions have been thought of as 'passions', because we are passive, not active, in experiencing emotions. We 'suffer' or 'undergo' them, rather than bring them about. It may be that we can make choices, e.g. about what kind of person to be, that will change our character and that will result in our having different emotions in the future. For example, we may choose to face our fears, to become more courageous, and then feel less or fewer fears in the future. But we cannot choose what to feel in the present. Or again, we may have some indirect control over what we feel, by focusing our attention on certain aspects of a situation rather than others. But we can't directly control, by choice, what we feel.
We do make moral choices as well. Given that we don't choose our emotions, it follows that when someone feels shame, this is not a moral choice they make. Instead, we might say that our moral choices apply to actions and perhaps to future character traits, like generosity or courage. Suppose, then, someone chooses to act in a way that then causes them to feel shame, e.g. perhaps they betray a secret they had promised to keep. They choose to betray the secret, but they didn't choose to feel shame. We can't choose what to feel ashamed of.
Perhaps this looks like a threat to moral autonomy. I don't think so. Perhaps the person thinks that it is not wrong to betray this secret (e.g. it could save someone's life). Then they feel shame, but they think that the shame is inappropriate - they don't think that they did anything wrong even though they feel shame. Our feelings and our moral judgments don't always line up.
This situation strikes me as quite normal, when in adulthood, we reject some of the moral rules of our childhood, e.g. someone who feels guilty at not going to church on a Sunday morning, even though they stopped believing in God years before.