there is, there are with personal pronouns

In a comment, John Lawler wrote:

Good question. First, the Bible quotation is from a translation, which isn't in Modern English, so it doesn't count. Modern English doesn't do that any more. Second, there is always inserted by a rule (called There-Insertion), and that rule has difficulty applying to personal pronouns because it presupposes existence and location, which is hardly an issue when saying I or they. In other words, there's no reason to use it when the subject already presupposes existence; it's irrelevant and therefore has marginal syntactic affordances.

Matthew 18:20

^KJV For where two or three are gathered together in my name, there am I in the midst of them.

^NRS For where two or three are gathered in my name, I am there among them."

In the biblical expression used here, whether it contains an inversion (KJV - Early Modern English) or not (NRS - Modern English), there is used as an adverb and not as a dummy subject, as it is the case in your example, There is me in this house (which, I agree, is unusual and may be possible in very particular contexts as indicated in the comments).

I don't speak Hebrew, but the Greek version of this expression [ἐκεῖ εἰμι - there am] confirms that there means in that place and functions as an adjunct of place. It is emphatic, the sentence could stand without it:

I am among them (NRS)

But in the KJV version, the omission of there will no longer require an inversion:

I am in the midst of them (KJV)

As for the use of there is/are with a personal pronoun, it is indeed rare, but not completely non-existent. A wild-card chart in GNgram shows you

1. that the use of there is me has recently seen a mild increase.
2. that often another word (preposition or adverb) will come between there is and the personal pronoun.

You can find it in literature, as a way of introducing a character:

There is me, and own God-Master. There is Slippers, and Slippers's Own God-Missus. That is all my paws. There is Adar. There is Cookey. (The Complete Works of Rudyard Kipling)

And you could probably use this expression while describing a photo or a video. This following excerpt seems to be describing a scene in a vivid way:

But no, instead there is a mere bishop, there is the king, there is me in a bewitching gown of gray-green silk that shifts colors as I move... (The Boleyn Inheritance by Philippa Gregory, Page 317).