Answer:
No, I don't think he's very trustworthy because throughout the story you can see how eccentric and crazy he is.
Explanation: I thought he was just telling the story as he experienced it firsthand, but it may not be the case. From the beginning, he tried to advocate for his own sanity, but the story he told completely undermined that and was inconsistent with his sanity statement. Throughout the story, he recalls the events that led him to murder the old man and then plead guilty.