It is very hard to get both unemployment and social security disability at the same time. This is because one of the necessities of unemployment benefits is to be actively looking for a job. You would have to please the unemployment office that you are able to fulfill their requirements.
The Social Security Administration and the Unemployment office can and will share information when they decide eligibility. In case you apply for both, you should be be prepared to explain how you will be able to abide by the unemployment's work requirements while also claiming a disability.