Financial talk

My mom and I are under welfare and we get food stamps every month, housing and free health care for me only since I'm 16 years of age. My mom says I can't get a job (unless it's under the counter job) because if I get a job, and they see we make more money than we do, they'll take my health insurance away. Is this true? I have no clue about this and I really need this question answered. Thanks!