Is there a confidential std testing clinic that doesn't have to report positives?

No: State laws require that any facility, lab, or physician that gets a positive report of certain STDs report it to the state department of health. Not doing so would be a criminal offense. Std results are not reported to any individual person or organization though so they only people that would know are you, your doctor, the lab, your insurance (if used), & possibly the state health department.