How do I apply for disability benefits without feeling ashamed?

The shame is worth naming first, because it is doing a lot of the damage. Needing help is not a moral failing. Benefits exist precisely for moments like the one you are in, and using them is no different from drawing on any other thing you have paid into or are entitled to. You are not asking for a favor. You are claiming a provision. The system feels impenetrable partly because it is complicated and partly because you are facing it alone and unwell. That is a bad combination for anyone. The wall looks smaller when someone who knows it stands beside you. You do not have to become an expert in the rules to get through them. So make the first move small: find one person or place whose job is to help people apply, an advocate, a disability charity, a legal aid line, and simply ask where to begin. Let them carry the parts that shame you. Your only task right now is to reach out once. Everything else can follow from there.