Simply covering up with acoustic foam wont make much of a difference, as you will still have to deal with low frequency standing waves which the foam will not absorb. Bottom line is - small room + parellel walls + hard boundary surfaces = bad sound.
However, the techniques you described - room in a room - is a common technique used by recording studios to isolate their rooms, building a room on top of insulating materials inside an existing room, so the idea is there. Just no glass please. You'll get an idea of how that will sound like by sticking your head in a fishbowl and saying HELLO.
A more cost effective idea is for you to get some acoustic underlays, and build another floor, preferably of a carpeted material on top of that. After that, some stratigically placed acoustic foam will more or less solve your acoustic problems. Nice thick curtains would help for your windows too. :wink:
All the best!
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