How can I stop noise coming through my walls without destroying my walls?

I live in a rental house with a mother in law unit. her unit shares a long wall with my Master suite. both of us have TV's mounted on the shared wall. We can clearly hear each other's tvs and when they are off, we can hear each other unclearly talking at a normal tone. If my husband and I fight, though, she... show more I live in a rental house with a mother in law unit. her unit shares a long wall with my Master suite. both of us have TV's mounted on the shared wall. We can clearly hear each other's tvs and when they are off, we can hear each other unclearly talking at a normal tone. If my husband and I fight, though, she can hear every word! We cannot alter the walls or damage them and those acoustical foam things look like heck. The fabric tweedy ones look nice but are so expensive. I heard of something from recycled newspaper covered with decorative fabric but can't find it. The one link in an article was dead. to make it more difficult, I am disabled, she is disabled and he is disabled! We live on extremely low fixed incomes and just getting moved in has left us broke for the rest of the month anyway. I do have a caregiver and a couple of friends who will do stuff but money is an issue as well as the issue of not damaging the walls or making the rooms look awful. The landlord thought corkboard could be painted but I haven't found it cheap enough I don't think.I have watched a few DIYs on youtube but sort of feel tired watching! lol... any suggestions?
Update: How can I stop noise coming through my walls without destroying my walls? ...Please see MY answer to everyone's answers: below
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