Actually is IS slander IF it fits these THREE things.
1. It is false
2. It is done with malicious intent, or is considered vile enough by normal standards that malicious intent can be implied.
3. It causes you financial loss.
Spreading the rumor of you having a mental illness is most DEFINITELY slanderous if false, and the damages sustained from an actual or perceived mental illness can be significant. According to Cornell University and the National Institute of Health, people with mental illness suffer more discrimination in employment and housing, than the discrimination of African Americans, Latinos, and women COMBINED!!! It's horrible, and the ignorance of the comments you've received to not help you take this head on only proves Cornell's point about society's thinking and utter ignorance regarding mental illness, and the degree of discrimination and damage it causes lives. It's already caused you stress. But you gotta be strong and nip this in the bud NOW or it could follow you from job to job.
The reason people don't hear of the degree of discrimination regarding the mentally ill, is because it is brushed aside as unimportant, (much like the comments you've received already), and because the mentally ill don't often march on Capitol Hill for their rights. These comments here are incorrect, and the loss of employment, or wages, or promotions you could face if allowed to continue could be substantial, and there's NUMEROUS CASES to prove it.
You sound young. If you are under age, find an adult to help you, a supervisor or a parent. If you are of adult age, report this behavior to the supervisor. If out of control enough already, talk to an attorney who will charge you $50 to send her a "cease and desist" letter. That usually educates workplace gossipers just how dimly the law views workplace defamation...and it does.
Do NOT believe this isn't important. It is! ESPECIALLY when it's gossip regarding false incriminating health issues. It is VERY SERIOUS. Health gossip is very destructive and if unchecked has caused tremendous stress and days lost from work, and it DOES set you up for discrimination. Workplace employee gossip of this degree is NOT to be brushed off as childish, it's damaging! TALK TO YOUR SUPERVISOR.