They may be administered by the local school board or by an independent contractor paid by the state.
I am also not sure who I should contact (my account manager, my recruiter, etc.), because this company is in a different state, and I work as an independent contractor at home and have never met any of the employees face-to-face.
Additionally, if you were working as an independent contractor rather than as an employee, you will not qualify for unemployment.
If you received a 1099, you were an independent contractor.
It's up to you to decide whether to formally set up your business as a corporation or sole proprietorship, or if you simply accept project work as an independent contractor.