Katniss does indeed have trust issues. In fact, she openly admits to readers in chapter 9 that she does not think putting trust in people is wise. Katniss sees trust as a weakness.
The Games begin in two days, and trust will only be a weakness.
Katniss isn't wrong with that trust assessment either, so her lack of trust works in her favor simply because of the nature of the Hunger Games themselves. Twenty-four tributes will go into the arena, and only one is supposed to come out alive. Trusting someone eventually means having to betray that person or be betrayed by them. Blindly trusting someone else's supposed altruism could lead her to a quick death. Trusting in herself and only in herself gives Katniss her best chance for survival. Her lack of trust allows Katniss to have a realistic view of her chances.
Katniss's lack of trust isn't something new for herself, either. She comes from one of the poorest districts. Food is scarce, and she has been raised knowing that selfishness is the standard operating procedure. Trusting someone to do something nice is met with suspicion. While I generally think that Katniss's lack of willingness to trust in people is what helps keep her physically alive in both her home district and in the games, I also think that her lack of trust ensures that she is emotionally distant from other people. Katniss doesn't fully trust anybody. Consequently, she is an emotional island and is lonely.