Do you have to give the health department your private insurance?

I'm a student (23) and still on my parent's insurance and I am having some gynecological problems that I need checked out but I do not want them to know. They will surely find out if I use their insurance. Is the health department safe and trustworthy? Do I have to provide them with my insurance information? The payment is on a sliding scale and you have to provide proof of income...will they just use my part-time job to determine what I pay? Point being is it possible to keep this from my parents at this stage if I go to the health department?
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What state are you in? Technically, i think that is illegal. I´m actually just curious of why the health dept. wants your private insurance. ¨stop lying¨
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