If you didn’t have sex with anyone else prior to that I’m the last few weeks I’d assume so
I see a second culture was done and came back negative, cultures can often show false negatives because if you don’t get it swabbed in time not enough of the virus might be present. To be sure you could go for a blood test and check in 12-16 weeks
Culture positive and blood test negative would be a recent infection. It takes a while for blood antibodies to show. If you were to test in a few weeks it would likely become positive on the blood test. I wouldn’t be concerned about HPV from a cream that someone with HPV used at some point
Sorry for errors. I was in a rush typing