I'm someone with a disability that people can't see. In my job interview tomorrow, do I have to tell the company about my disability in the interview?

No. Applicants and employees are not required to share this information, unless requesting a reasonable accommodation or modification in how they participate in a job interview or perform essential job functions or tasks. Under Title I (Employment Provisions) of the Americans with Disabilities Act (ADA), disclosing or telling an employer that you have a disability is a personal choice.

If you do not need/want to request an accommodation, you never need to disclose your disability. If you do want to make an accommodation request, this can be done at any time during the hiring process (before the interview, during the interview, and after you are offered the job and before you start). You can also ask for an accommodation at any point during your employment if you find you need it.