Welcome to the Forum.. As I read your description I felt that it really did not sound like HSV and as I read on and saw your test results this was confirmed by your laboratory tests. You do not have herpes. There is no need for further testing.
Let me provide a little bit of background as well. HSV infections are very common (over 20% of adults have genital herpes and most who have it do not know it) so there is a fair possibility that you could have had sex other times with persons who had HSV and did not get it. This is not too much of a surprise. It turns out that most exposures to sex partners who have HSV and do not have lesions that they are aware of do not lead to transmission of infection. In fact, some experts estimate the risk of getting herpes from an asymptomatic partner who has the infection as being between 1 in a thousand and 1 in 10,000 with many feeling that the accurate estimate is probably closer to the 1 in 10,000 figure.
As for the "lesion" that you noticed, let me please remind you that the skin on the penis is rather thin and therefore fragile and that it is susceptible to the sorts of friction-related damage that occurs with masturbation or vigorous sex. the lesion that you described sounds like this ..If this is what was there., that when you removed the overlying skin is was a bit shiny.
The lesions of fungal skin infections or eczema can resemble each other and what you describe could well be either or both.
This, having provided this as background, let me answer your specific questions briefly:
1. I see no need for further testing for HSV.
2. Eczema and fungal skin infections are possibilities as your doctors have told you.
3. No, herpes cannot cause eczema.
I hoe these comments are helpful to you. EWH
Ha, there is a typo above. My dermatologist gave me VANOS for my eczema, not Zocor. I think there was a zocor commercial on while i as posting!