CONSTANCE: People often feel guilty over something they never did. It usually goes back to their childhood. The child often wishes something terrible would happen to someone, and if something does happen to that person, the child believes he's caused it. Then he grows up with a guilt complex over a sin that was only a child's bad dream.
Constance is here explaining how guilt complexes work. Note—this is notnecessarily a medically accurate description of guilt complexes. Children can believe they're responsible for bad things happening, but that doesn't mean they'll get amnesia and a guilt complex later on; nor do people with delusions always have some sort of guilt trauma in their childhood. But this pseudo-psychological explanation provides a fun plot for a film, and that's what really matters.
MURCHISON: Our Dr. Edwardes turns out to be a paranoid impostor. He's very likely guilty of having murdered the real Edwardes.
Ballantyne is guilty of murdering Edwardes; he feels bad about it and responsible for it. But whatever he feels, he isn't actually the guilty one: Murchison is. The two kinds of guilt—feeling bad and actually responsible—are split up throughout the film. If you feel bad, you didn't do it; if you don't feel bad, you did.
CONSTANCE: You insist without proof that you're a murderer. You know what that is, don't you? Whoever you are, it's a guilt complex that speaks for you. A guilt fantasy that goes way back to your childhood.
Constance says that Ballantyne's guilt complex is speaking for him. His childhood delusions have possessed him, and taken him over. He's not a man at all, but a bundle of childhood anxieties… which is why Constance needs to take care of him. When he's cured, he'll go back to being that Hollywood leading man he's supposed to be. Mental illness, here, means not being a grown-up.
CONSTANCE: Your guilt fantasies were obviously inflamed by your duties as a soldier.
Constance's comment here suggests that Ballantyne didn't like to kill because of something wrong in his childhood. In other words, most people should not, or do not, feel guilty for killing in war. At the same time, the film raises the possibility that a man who kills in wartime could be affected, and pained, by his own actions. The themes aren't quite confronted directly, but they seem like things that would be in a lot of people's minds when Spellbound came out just a few months after the end of World War II.
BALLANTYNE: I didn't kill my brother. It was an accident. It was an accident!
CONSTANCE: That's what's haunted you all your life. That was the memory you were afraid of.
This seems too easy, doesn't it? Ballantyne remembers he accidentally killed his brother, and it's been tormenting him all his life, but suddenly he realizes it wasn't his fault, and he's all happy and free? He even shouts happily about it.
Not that we want him to be sad, but surely he'd still be a little distressed? Oh well; maybe Hitchcock was just sick of him moping around all the time.