Will Viral Culture Help To Detect HSV1 Genital Infection?

I took a blood test and came back negative for everything except HSV1. The HSV2 test was negative. I get oral cold sores regularly and have since a child. I have never had HSV1 symptoms genitally. However, my ex had culture done for HSV1 and he tested positive and since has had breakouts. We were careful and did not have sex during those times but did engage in unprotected sex at other times. I am worried of the possibility that he may have infected me with HSV1 genitally. If I do a viral culture, will it be able to tell me if I have HSV1 genitally? I understand that it often comes back as a false negative and so if it is negative that doesn t necessarily mean I do not have HSV1 genitally. But what is the likelihood of having contracted it? Is it worth it to do the test? Should I be concerned of infecting future partners? I also heard that if a person does contract HSV1 genitally, it will clear in a year and it will not show symptoms again. If that happens, can you still contract it after the first year?