Can you apply for UI? Sure you can. Anyone can apply. There's no law blocking them from doing so.
Whether you will be approved for UI if you quit your job is questionable, however, particularly if you are doing so because of a medical condition that makes it difficult or impossible to work. In order to receive UI, you need to be able to work, actively looking for work and able to accept work if offered.
You are more fortunate than most because you are in one of the very few states where there are state-provided disability benefits. If you are unable to work because on an ongoing or chronic illness, disability benefits would be a better bet than UI.