Finnick and Annie were always together and were seemingly joined at the hip. They were always touching and keeping a physical connection in some way: linking arms, holding hands. It was almost as if they were afraid to let go of one another.
In Annie's head, that was exactly the case. She felt terrified that if she were to release her grip on Finnick, someone would take him away from her or vice versa. The thought of being left alone to deal with the confines of her mind was unbearable to Annie, but she felt powerless, like she couldn't keep Finnick, her only source of happiness, to herself. Like she couldn't protect herself.
In Finnick's head, he was also fearful, but for a different reason. See, he had always felt very protective of Annie, and he knows that she's aware of that. He's glad, actually. It humbles him to know that Annie knows that he's there for her. He would do anything and everything in his power to protect her, even if it meant sacrificing his own life. As pessimistic and masochistic as it is, he'd even thought about it a few times, what it would be like to die for her. He'd thought about when it would happen, how painful it would be, and if he would fight back or not. He didn't care what the situation was. He decided, resolutely, that he would fight for her in sickness or in health, in extreme pain, and on his weakest and worst day.
If Annie wanted to stay inside and relax, Finnick was more than glad to oblige. If Finnick wanted to go to the beach and collect seashells or catch fish, Annie was there. Nothing that anyone did could ever keep them apart. It was like they were destined to come in a pair, like two peas in a pod. Cookies and milk. Peanut butter and jelly. No matter how you look at it, they were undoubtedly meant to be together.