What Causes Red And Itchy Patch On Penile Tip While Having Eczema?

HI I haven t had sex. But I ve come in contact with my partners vagina alot from when we we sleep naked together and so forth. I recently have gotten a red dry patch on the tip of my penis and It was itchy... but I also go dry patches all over my body bc I have eczema. The patch on my penis went away after using cortizone gel. Do you think patch on my penis is from eczema or I could have std?