Hi ladycharm (great name, by the way),
There is no such national registry, and I'd be very wary were you to find a resource that claims to offer any sort of comprehensive data base in this regard.
The problem, well one of them, is that many STIs are not diagnosed and when they are, typically do not involve individual name reporting. About 85% of HSV cases are undiagnosed, and as many as 25% of these with HIV are estimated to not be aware. "Reporting" usually means just forwarding along number of diagnosed cases per locale, not a list of names. Keep in mind, too, that just because someone's ex has/had an STI doesn't mean their partner contracted it. If it's a bacterial STI (like chlamydia, gonorrhea, or syphilis), the infection can be cured with proper treatment.
Your idea of going for STI testing is a good one. Talk with your health care provider to see what they recommend. Any battery of tests should include HIV and probably chlamydia.
This resource is geared more towards college students, but has good STI testing info all the same and includes a section on talking with a partner:http://www.itsyoursexlife.com/gyt?utm_source=gytnow
I hope this helps. Post again anytime.