You can grow to be Large sized.
First, let's dismiss concerns about your girth: recall that the 10' x 10' square that your creature "occupies" in the horizontal plane is a matter of space you influence, not that you occupy. (PHB p.191, "Space") So you don't have to be a 10' cube to have a 2"-square mini.
The tallest playable race are Goliaths (EEPC, p.10), Medium humanoids standing 7-8 feet tall.
But then we look to the archetypal Large humanoid, the Ogre, and that stands 9-10 feet tall (MM pp.7, "Size" and 237, "Ogre").
So, at 9'3"...
You're Large now.
As for advantages and disadvantages, you've got all the features of a Large creature
- you have to squeeze (PHB p.192) to move down a 5' hallway,
- you can be mounted--if willing--by Medium creatures (PHB p.198), or even being treated as terrain by a Small or Tiny creature (DMB p.271, if your GM wants to use that option).
- your reach doesn't get larger--the Ogre still has a 5' reach--but you sorta-do have a larger reach that's being modeled by your Large size's 10'x10' footprint
- you might be able to argue for increased damage: see, for comparison, the enlarge spell's damage effect or the way an ogre's greatclub does 2d8 damage instead of the 1d8 listed in the PHB's "Weapons" list.
A census of Large monsters:
There are approximately 133 Large creatures described in the Monster Manual. Only the following say anything about their size other than being listed as Large creatures:
- Planetar: "they tower over humanoids" (p. 17)
- Barlgura: "standing just under 8' tall" (p. 52)
- Horned devil: "stands as tall as an ogre" (p. 69)
- Ogre: "stands between nine and ten feet tall" (p. 237)
- Shambling mound: "looms up half again as tall as a human" (p. 270)
So there's not a lot to go on: nine-footers are certainly large, but some up-to-eight-footers (Goliaths) are Medium, some just-under-eight-footers (Barlgura) are Large. If there's a line, it's somewhere between 8'0" and 9'0".