Not according to the script
To my knowledge no film canon exists that says Peter Parker was manic or anything like that. As KutuluMike mentioned, having a sort of "evidence wall" full of newspaper clippings and strings, pins, and tape everywhere is a common trope used in Hollywood. It's a colorful visual way to show the audience what the person has been thinking about and obsessing over. Yes, it can mean the person is manic or crazy, but it can also simply mean that the person is really smart and is looking for hidden clues that others (without an evidence wall) would miss.
The film's script simply calls it a "wall of information":
[Aunt May is sitting in Peter's room looking at the wall of information he's created about his missing parents] ... [the information he'd stuck to his wall about his parent]
The notes/directions in the script don't mention words like "manic", "crazy", or "obsessed" when referring to Parker or his wall of information
In contrast, the script does mention one character, Max Dillon, as having an "obsessive" collection and that same character does in fact become unhinged in the film and looses it:
[inside his apartment Max has an obsessive collection of Spider-Man paraphernalia]
So the lack of and similar language used by the script to describe Parker or his wall of information, I would seem that the filmmakers were not trying to show Parker to be in any sort of manic or schizophrenic condition.
It is far more likely that we are meant to understand that Peter's wall of information is simply a manifestation of his desire to investigate and solve the mystery. Peter isn't just a little curious about his parents, he's really delving deep to find all the connections and clues that he can, hence his use of the wall of information to help organize his thoughts. The wall also serves as a visual representation of his thoughts and efforts for the benefit of the viewers.
TL;DR: The wall of info means Peter is digging deep to find answers and connections that might help him solve the mystery.