If you want to reduce how audible you are outside your room you can add some sound dampening material to your walls and door and seal air cracks around your door. Those black spiked foam wall panels or heavy curtains are probably best for sound dampening, but something as simple and cheap as paper egg cartons on your walls will greatly reduce how much sound gets through.
So, there's a difference between sound absorption and soundproofing. Curtains and foam panels can do wonders for making your room sound better acoustically but won't do much to lower the amount of sound getting out. The only way to actually soundproof is either by adding a bunch of mass (bricks/concrete blocks/mass loaded vinyl) or by creating air gaps (or some combination of the two). Conflating soundproofing and sound absorption is very common but they are different. . Paper egg cartons will do little to nothing for either sound absorption or soundproofing; this myth comes from old style sound absorption foam tiles that kinda looked like egg cartons and were therefore referred to as such.
You're absolutely right about sealing door gaps helping though.