STI testing

I've been doing a lot of research lately about how to get STI tested for free and I still have questions. I myself have no symptoms and have never been tested by a medical professional, but I have donated blood and I know they would have called to notify me if my donation was compromised. I know they don't test for all STI's though so I'm wondering which ones should I be tested for that are not found in the blood? Will the Health Department test me for free? Respectful replies appreciated. :)