All three words obviously have multiple meanings, but in the context you're taking about, specific and particular are completely interchangeable in every case I can think of.
Certain is slightly more nuanced. It can (but doesn't always) carry a sense of deliberate ambiguity. For example, I'm here looking for a certain person could mean:
- (neutrally) I'm here looking for a specific person
- (enigmaticaly) I'm here looking for a specific person, but I'm not going to say who because it's a secret
- (ironically or humorously) I'm here looking for a specific person, and you know who that is, but I'm not going to mention their name (for example because they and I recently had an argument).
Context and tone would make clear which of these was intended.
Personally, for that reason, I would avoid using certain in the context you're describing. A dictionary will tell you it's correct, but it doesn't feel quite as natural or idiomatic as specific or particular.