"Soundproofing" is a bit of a misnomer in the sense that it is any attempt at noise reduction by definition. And, it is not realistically possible to completely soundproof a room (meaning to cancel 100% of sound entering into or escaping from a chamber,) at least not on any pocket-friendly budget or with non-professional design and labor.
For example, Orfield Labs' anechoic chamber and Microsoft's 'quietest place on Earth' have a background noise measured in negative decibels. Each took years to design and a LOT of $$$ to ultimately realize... And, they are technically still around 99.99% soundproof, or something like this.
That said, there are a few things you can try if this is still an issue 3 years later... I'd start by searching the web for 'DIY Soundproofing' or 'soundproof closet,' instead of searching for any form of 'vocal booth;' which is going to assume that you are more concerned with keeping noise from entering the booth than you are of noise escaping the chamber (though the same result is achieved either way, arguably.)
Firstly, sound travels upward much more efficiently than downward; so, you are better off if you can get above your neighbors. Secondly, you want to try to reduce noise through absorption as much as possible (since you cannot increase distance from your neighbors...) If you go the route of soundproofing a closet, you will need to add a lot of absorbent material to the floors, walls, door(s), and ceiling. From there, you can, and should, build your 'human-sized box' inside this closet and add even more absorbent material to the inside and outside of that.
Finally, and unfortunately, you are not likely to find a very efficient or cost-effective solution to your problem...Unless you have a big budget, you are much better off to find a solution that is away from the property. It is simply not realistic to think that you can soundproof a room enough in order to avoid disturbing a sleeping child inside a house in which you are shouting... If you absolutely cannot find an off-property solution, then you are better-off building your soundproof closet in some sort of outbuilding like a shed or garage or bomb-shelter. :)