Is it correct to write I am Gerardo and I am here. or I am Gerardo and I'm here. Is there any difference between these two statements?
As you can see from this discussion, their meaning is semantically identical, but the contraction indicates informality relative to the non-contracted form.
As FumbleFingers mentions in another comment, "I am" has an additional attribute that "I'm" lacks. When "I am" is used as an affirmative response, it can imply an echo of the query:
Who is X? I am. [Implying "I am X".]
Whereas "I'm" requires echoing the query:
Who is X? I'm X.
Semantically, they're the same. But in many contexts they differ pragmatically. Imagine a large, though not very lavish, convention. Several mikes traverse the numerous audience, for which there aren't enough lights, so they're pretty much in the dark. Somebody takes the mike and says something truly interesting. The guests on stage squint and strain their necks trying to make out who it was. The spotlight hunts for its target as the voice resounds through the speakers: 'I am Gerardo and I'm here.' In that context, Gerardo is referring to his exact location. Now, if Gerardo happened to be a name notoriously known to belog to a public enemy, say, someone like Unabomber, and if his mere presence at the convention, say, in Washington DC, meant a threat par excellence, he'd be much more likely to have said: I am Gerardo and I am here. In that context, Gerardo is referring to his general presence at the convention, not to his exact location.
So, both the constructions have their distinctions, even if they be only pragmatic.