Is genital herpes cureable? How long will it take? My HIV test was found negative.

Unfortunately, "herpes is forever" is all too true. On a brighter note, it can be successfully suppressed with anti-viral drugs, either with each flare, if infrequent, or with long-term suppression. Since herpes lesions compromise the integrity of skin/mucous membranes, it puts you at greater risk for acquiring hiv. Thus, always use protection & practice safe sex. See pcp for rx for anti-viral meds.