Earth starfleet

Question

My understanding is that while Starfleet originally grew out of the United Earth, Starfleet now acts as the military arm of the Federation as a whole.

Despite this, I've noticed that some Federation members (Benzites and Vulcans come to mind) also maintain their own internal Starfleets separate from the Federation. Has there ever been any indication of earth having its own internal forces since the UFP came into being?

Answer 1

I'll address several points in your question individually:

1. "Starfleet originally grew out of the United Earth": this is correct - Starfleet did start out as the space exploration and defence body for United Earth (Source)
2. "Starfleet now acts as the military arm of the Federation as a whole": this is partly correct. Starfleet (following the foundation of the United Federation of Planets) is a body of the United Federation of Planets rather than just Earth. It is not, however, just a military arm. I direct you to @Richard's outstanding answer to this question which explains that, whilst it is true that it has a military capacity, it's primary function is exploration.
3. (Your main question) "Has there ever been any indication of Earth having its own internal forces since the UFP came into being?" - no. Looking at this list of militaries we know of, 'United Earth' only has two - Starfleet (following the founding of the Federation) and Military Assault Command Operations, which was prior to the founding of the Federation.

So, in short, no, there is no indication of Earth having its own 'Starfleet'. It indeed may have had a local defence force that resided on the planet, but this would most likely not have had the space capabilities or resources of Starfleet.