Confident I have chlamydia/gonorrhea – how to deal with insurance, parents, and finances while getting tested?

Hi all, I've never been to a clinic on my own before, and I am absolutely *terrified* of hospitals and I'm unsure how to handle finances. Here is my situation:

I have mild burning when I pee and some pussy discharge from my penis just 1 day after having unprotected sex (I was the top). It looks like this is chlamydia, gonorrhea, or urethritis. I'm unsure how to distinguish between the three.

I am mortally terrified of injections, IV's or being penetrated in any way. I thought the "swab" tests would just be like getting your throat swabbed, but when I looked them up, they look horrific. Does getting tested hurt? Just for a chlamydia/gonorrhea test will I have to provide blood?

Secondly, and more importantly, I don't know how I'm going to pay for this. I have insurance (paid by my parents), but I don't want my parents finding out about this – will they know if I use insurance to get an STD test? More importantly, how do I initiate any of this? I walk into a clinic, give them a credit card and insurance info, and how do I know when/how much I will be charged? If this is going to cost me more than $100, I'm turning around and walking out of there, period. I get evicted in a few days and I cannot afford a place to live if this is too expensive.

In summary, I have 2 basic questions – 1) will getting the test hurt? and 2) How do I go about paying for the test, and how do I know when/how much I will be charged?

Thanks for your help and advice. I'm very scared but I'm sure I'll be okay.

UPDATE: I visited my school's health services instead of Planned Parenthood. I described my symptoms and provided a urine sample, but didn't have to get blood drawn or use a urethral swab, which was nice (they directed me to another health center where I should go to get swabbed for an HIV test). I had to get a shot on my butt (antibiotic for gonorrhea) and I have to take antibiotics for chlamydia for the week, but the visit really wasn't that bad. Hopefully it was gonorrhea, cause my symptoms are already clearing up. I provided all insurance info, so I haven't had to pay anything yet actually, but I have to pick up my prescription for maybe ~$30 ($45 without insurance). Overall, not very expensive, not very painful, and 100% worth it. Thanks for your advice!