I'd say 'disappointed in' is usually for persons: When he got more than half the answers wrong, his teacher was disappointed in him.
And I agree with Bob that 'disappointed by' is the passive voice, which usually emphasizes the action more than the result. If you say 'I was disappointed by X,' you mean 'X disappointed me.' With a person, you might even almost expect a reference to something specific that happened: I was disappointed by Fred today. He said he would call, but he never did. However, that sounds artificial because it would be more natural just to use the active verb.
In a more general sense, with things, I agree with Bob and Lara that you can use any of several prepositions: not only 'by' and 'in' but also 'about,' 'with,' and even 'over.'
'With' (or 'by' or 'in') is often a judgment about the quality of a specific thing: The salad was good, but I was disappointed with the main course.
'About,' and even more so 'over,' tend to convey a broad general impression, a reaction to an entire situation: I'm disappointed about the direction our country seems to be heading; I was really disappointed over the whole way they handled the layoffs at work.
As for 'to be/feel sick about sth.,' it might not be common in BE, but I don't think anyone could possibly confuse it with throwing up. It doesn't just mean disappointed but deeply disappointed; to be sick at heart, to feel terrible about something, especially terribly sorry: Oh, no, I can't believe your car was stolen again. I'm just sick about (/over) that.
OT @Martina: If you're new to the forum, have you considered registering and/or adding something to your nick, like an initial or a number or a geographic abbreviation? I believe there's at least one other Martina who's already a fairly regular participant.