"My daughter is dyslexic, but her school told me that our county doesn’t recognize dyslexia as a disability."
Dyslexia, as well as other learning disabilities, is covered under the Individuals with Disabilities Education Act (IDEA). If your school told you otherwise, they are wrong.
Having said that, I remind you that a diagnosis of dyslexia, ADHD, or other disability is not enough to guarantee services or accommodations. Both IDEA and Section 504 of the Rehabilitation Act require that your doctor show that your daughter’s dyslexia impairs a major life activity, like academic performance. He should establish that fact in his evaluation.
If the school does not comply with the law after you supply documentation, you should file for an impartial due process hearing, in which a state-appointed hearing officer will determine whether the school is legally required to provide accommodations for your daughter.