Holden suffers from depression. It is likely that his self-esteem was never really high, and as a result he looked up to his brother Allie and wished that he could be more like him. When Holden writes the composition for Stradlater, he says that Allie was the kid whom everyone wanted around, and his statement implies that he wishes he were more like his brother in this regard. So when Allie dies, Holden cannot understand why such a good kid would die when he could have died instead. Holden does not feel like he can live up to Allie's memory, and the irrational guilt eats away at him. Holden should have gone to see a therapist or psychologist, but his parents never sent him for help. Holden's depression eats away at him, and he starts to project these feelings onto other aspects of his life. For example, Holden has a hard time with change, hence his love for the museum which never changes. In the end, Holden learns that opening up to others will allow him to deal with his depression.
Holden appears to be suffering from PTSD stemming from the death of his brother and from witnessing the suicide of his schoolmate who bailed out of a dorm window wearing the sweater Holden loaned him.
The symptoms of PTSD that Holden exhibits: depression, inability to concentrate, crying, uncontrollable rage, lack of motivation, sleeplessness, etc. (I'm intimately familiar with these symptoms because I was diagnosed with PTSD stemming from childhood trauma.)
Given Holden's apparent high intelligence and cultural sophisitication, he was high functioning until confronted with these two taumas, which lends further credence to the theory that he suffered from PTSD stemming from them.