Mental illnesses are disabilities, but whether or not you are "disabled" depends on the context and the severity and your ability to compensate, etc. If you want to collect "disability" pay, you may have to prove that you are so disabled that you can't work, and even so, the amount that they pay depends on a baseline you have established on the basis of past earnings or sometimes on your parents' standard of living or other if you are a dependent. It can be a difficult process and can take years before you start getting disability income.

On the other hand, you may qualify for services that support you in being able to work, and mental illness is generally considered a "qualifying disability." For example, vocational rehabilitation may provide therapy, medical treatment, etc., as well as training, education - whatever they determine would help you with employment. In my state, there is a program where you can be on a list for priority hiring for state jobs. My understanding is that the employer isn't told what the qualifying disability is, but they know generally that people on that list qualify on the basis of a disability.

You need to be judicious about who you tell about having a disability, and about the context. Don't use it as an excuse - that perpetuates stigma and makes you look irresponsible. We need to show that we are willing to do what it takes to overcome our challenges and be responsible for what we do or don't do.