If you’re looking for a low-cost solution, I would suggest homasote. Generally, you would want to use this under your drywall, but it can be applied directly to walls as well. I lived in a converted living room for a while and to create the room I used two layers of homasote on the back of fitted ikea shelves and the sound insulation was fantastic. It was better than the drywall and door I constructed for the rest of the room. Homasote is just compressed fibers, so it looks very urban/modern and can be used like a pin board. I have a real bedroom now, but I still use a huge sheet of homasote as pin board because it looks so cool, and is extremely functional. If you’re even remotely handy with a skill saw and a hammer, you’ll be golden. And if not, you can probably get the hardware store to cut it to your exact measurements and I’m sure craigslist probably has a number hammer friendly workers at the ready. Hope this helped and good luck!