Welcome to the forum.
There has been a lot of research in recent years on oral HPV and the association of a single genital HPV type (HPV-16) with throat cancer. Although a lot is to be learned, the important facts are that oral HPV is a lot less common than genital; and that the vast majority of people with oral HPV-16 infections (probably under 1 in several thousand) actually develop cancer.
There are indeed tests that can attempt to diagnose oral HPV and even determine the type, and you can find them on line. However, they have not been certified or approved by the Food and Drug Administration and are not recommended by most experts, even in people possibly exposed orally to the virus. In any case, the ONLY type you need be concerned about is HPV-16, and even that really shouldn't be a worry. At this point, I do not recommend that people in your situation take any precautions at all. Certainly the details of how you kiss, or the mechanical details of oral sex, are not likely to make any difference; indeed, I doubt we'll ever know whether, for example, more or less tongue contact has any effect on HIV transmission risk -- this would be almost impossible to study. There also are no data on genital to roal transmission risk for any single exposure.
Bottom line: If I were in your situation, I would do nothing at all. I would not be tested for HIV, would not use a condom, and would continue oral sex any and all other sexual practices that I and my partner both found enjoyable. And I would not seek to learn my partner's HPV type (which likely isn't known anyway -- most tests associated with pap smears simply group HPV as "high" or "low" risk, without information on the specific type.
Here are three other threads that go into greater detail on all these issues.
Best wishes-- HHH, MD