The blanket wont make much of a difference, it is more for the acoustics(the way the room sounds), which is a whole different thing. They are false advertising it. The best place to start, i believe, is sealing all the places where air will leak, ie. around doors with rubber seals, and if your doors are really light i suggest adding a layer of MDF, (like the picture). Secondly if you have any windows block them up. If you can't permenantly, make a plug out of MDF, with rubber seals round, the exact size of the window frame, so that it just slots in(like pic). If your windows don't allow for this, make "shutters" out of MDF with magnets strips all the way round them and on the windows(like pic). If you have any holes or gaps in the walls or round borders/frames fill these with caulk. You sound now have an airtight room, which should help in soundproofing, not fully, but it may be enough for what you need. If not, you will have to add mass, eg. a second wall, (made from drywall) which is separated from the existing wall with an air gap, which means lots of work, effort, and money. Ok, so if what i first suggested is sufficient, then great, only thing is, you will have to breathe. I will let someone else handle the breathing problem, as i am unsure.
Don't worry though, there are "remission" days. 
