Hello, LandingSanely! The answer is "yes" generally. Here's the technical information for the US Social Security Administration -
Social Security Online, Disability Programs: 12.00 Mental Disorders - Adult. Other countries have their own mental disorders disability programs.
Frankly, it's a complicated, often lengthy process. I've heard stories of people applying for disability and simply giving up the quest because, given their illnesses, they just don't have the focus or energy to complete the process. Others make it through the application process; the vast majority of those are turned down - or so it seems to me. (I imagine the disability bureaucrats joking with one another: "Hey, this person correctly got through the disability application process - that proves they're not disabled!") Some of those who get turned down seek out lawyers specializing in disability claims and, like magic, the majority of those claims are accepted. The lawyers take as their pay a percentage of the the lump sum you first receive from the government; if your claim is approved, you're paid from the date of the application up to a year prior, and the percentage the lawyers can take is set by law.
No, you don't have to go it alone first, you can go straight to a disability claims lawyer.
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My dog

mastered the "fetch" command. He would communicate he wanted something, and I would fetch it.