Welcome to the forum. I'm answering in the belief you are female, but you don't say so directly either here or on your profile.
First, it is statistically unlikely your partner had gonorrhea, which rarely causes asymptomatic genital infection in men. If he had gonorrhea, he probably would have noticed quite obvious symptoms (pus dripping from his penis), and you likely would have seen it as well. Second, pharyngeal gonorrhea is generally without symptoms, clears up on its own without treatment, and is not commonly transmitted to partners. There are exceptions to these rules, but they are uncommon.
Still, it is too bad none of your local resources offers pharyngeal gonorrhea testing. Although testing really isn't necessary from a medical or risk assessment perspective, obviously it would be reassuring for you to have a negative test result. Most likely the reason isn't simply intransigence, but the test methods available to the local clinics and laboratories. Thay may no longer use culture test, which is the only one approved for pharygeal testing; the NAAT assays most commonly used are not approved for the pharynx. If you want testing, a private physician's office may be the only option. However, it should not be costly, and your health insurance probably will cover the office visit and testing. (And no, you should not worry about confidentiality of such data. Insurance companies and medical offices are very good at keeping personal information private; the federal fine for inappropriate disclosure starts at $5,000 and goes up from there!)
Having said all that, I really believe your risk is sufficiently low that no testing is really required. If I were in your situation, I wouldn't do it and would continue unprotected sex with my wife (or male partner, if I were gay) without fear of transmission. But if you still wish to proceed, another alternative is to convince your partner to be tested. All it would take is a urine specimen; assuming he doesn't have urethral gonorrhea, you will know you were not at risk and can stop worrying about it.
I hope this helps. Best wishes-- HHH, MD
Sorry that I spaced out on your comment about not having health insurance. I really don't think your risk is high enough to worry about this or to spend anything out of pocket, especially if your finances are tight.