Quoting Jax in the Tardis:" What's the process like when applying for a child?"
Get out your phonebook, look for a disability lawyer. Hire him. Many doctor appointments will follow then there is a court date which you may or may not have to show up to.
I get ssi. I was injured as a child. My mom hired me a disability lawyer. I have had 14+ mris, xrays, and ct scans. I have a disk from a hospital with my mri. I handed that over to my lawyer and I won within a few months. I also had been seeing like 10 doctors so the lawyer contacted the doctors for my records from them. I never went to the hearing.... They might deny you the first time, but don't sweat it. They usually do deny people the first time.