Just before saying it, the speaker states that something nagged at her, like a memory, so when she concludes the exchange with "so I have", she is emphasizing the fact that there is more to the story. The reader might also perceive that the writer is annoyed that the person she's speaking to doesn't take any further action or do anything about what she shared with him.

In this context it means "yes i have".

You also will hear people using the phrase eg I've got nice eyes, so I have. It's probably best not to minic that example just there in written form when learning English but you will hear it spoken in some areas of the country if you travelled.