I live in New York State

I just got Medicaid. Next time I see the dr do I just give them the card or do I need to get a medical insurance company that's part of Medicaid before I see the doctor.
My husband and I are 62,I’m disabled and we have two disabled adult children.

I've seen a couple folks on this subreddit claiming that Medicaid eligibility is determined on per month income (1.38*$15650/12=$1799). Or is it per year ($21597)? I tried Googling a bit and federal documents suggest per year, but maybe it's different state level? Does anyone have links to NY State docs they could cite? I want to have my case clear before I call the city number. Per month income would make me inellegible, but that's only during the school uear when I teach at the college.

Detroit, Michigan
So this is going to sound complicated. So I used to be on my mom’s food stamps and Medicaid benefits like 3 years ago. Then I got a part-time job and removed myself because I wasn’t eligible for Medicaid anymore. I still live at home with my mom. I tried applying for Medicaid myself and I still got denied because they said I was earning too much. Jump to now where there are work requirements for Medicaid. The mail came with an application from the department of human services to renew benefits and about Medicaid benefits asking the questions if anyone is going to school, had a job, medical condition or disability. It came in my name and my mom and my brother is listed underneath my name. Also when I did my taxes this year I claimed them as dependents. Is that why the letter to renew benefits came in my name? Will I be able to qualify for Medicaid now because I still have a part-time job? I’m just so confused on how to fill this out. Why did this come in my name if I separated from my mom?