Before this becomes a runaway train...
What exactly do you think is wrong with your vocals that a booth or involved room treatment will make significantly better?
Can you explain?
I think you're doing a knee-jerk and opting for a nuts-n-bolts "solution", when I bet your vocals have issues other than the "room".
IOW...there's no way all your other tracks or great except for the vocals, because of the "room". If you have room issues, you'll have problems with all the instruemnts long before you have problems with just the vocal (unless you are recording everything else as synths or with DI setups).
Sure, proper room treatment is always a positive thing, but I don't think that alone is going to make huge difference in just your singing/vocal quality...except if you're Barbara Streisand, and everything else is already perfect other than the room.
Unless your room is an empty hull, with all kinds of flutter echo and nasty spikes (which I doubt, as most bedrooms have furniture, carpet, "stuff")...you might want to work on mic position, signal chain, and most of all, singing technique...
...before building anything.
Most home rooms have one or two good "spots" for doing vocals. You can put up a portable screen/gobo type affair if you want to knock off some early wall reflections. There's all kinds of ready-made contraptions that you can buy...or just make one yourself. It can be as simple as a blanket/quilt hung a few feet away from your singing position, and between you and the nearest wall.