Can inferiority complex be seen as an informal fallacy?

A complex itself? No, that's an issue for psychology, not logic.

However, are you trying to refer to the manifestation of such a complex, which may result in the person having it denying that they have it?

Dr Bo was wondering about the argument form, and I imagine something like this:

Gemma: I hate Chloe. She's always acting like she's better than me when she isn't. (1)

Also Gemma: Chloe is better than me at X and Y. I should try to learn from her. (2)

If (1) refers to Chloe being better at something, then this looks like conflicting conditions - Gemma is saying that Chloe isn't better than her (at anything), and then says that Chloe is better than her (at something). This is better referred to as doublethink though, as Gemma - and most people - are not logically oblivious enough to say an outright contradiction like that. 

If Chloe really is better at certain things than Gemma, and she says (1), then this looks like a person in denial. But again, that's not a fallacy.

So I suspected somewhat correct, that it contains a fallacy rather than being one itself.

The fallacy of self-contradiction. "I am better than that person. I want to be like that person."

Yes inferiority complex is a psychological condition and seems to be commonly loaded with the fallacy of self-contradiction.

Probably not. Rather it contains the fallacy of self-contradiction. As I suspected and others suggest.