There is a definite possibility this is bacterial but sores that scab are a little worrisome. Did your doctor swab the sores? Even if they had scabs, she should have swabbed them. There might not of been much material for her to get from the sore but she should have regardless.
It’s a good thing that your partner’s test came back negative. The one thing to note about hsv testing is it’s vert reliable for HSV2 if done 12 weeks out from a sexual encounter. So if your partner has not had sex with anyone but you within the past 12 weeks, then her HSV2 result for her is solid. HSV1 testing is not as accurate. Unfortunately, the IgG test for HSV1 misses upto 30% of infections.
If she’s ever had cold sores, then that is HSV one. So many people with HSV one have no idea that they have it because the symptoms are so minor, that they attribute it to something else.
If you get any further sores or marks on your penis, I would go to the doctor immediately or even go to an urgent care. Be seen as soon as you notice them. I would demand your doctor swab them. A PCR swab does not return false positives. They can have false negatives, if the sores are healing and their isn’t enough of a virus to be detected.
Are the antibiotics helping? If they clear things up, then it probably is bacterial but just keep an eye on things and if the sores appear again or you have any other symptoms, be seen. Good luck!