I'm not a doctor, but if you had this quick a reaction I doubt it was an STD, rather a skin reaction.
Years ago I also had a terrible skin rash on my cock. In my case I believe I contacted poison ivy or something similar on my hands, which was transferred to my cock, and the skin on the cock seemed much more sensitive so had a much more severe reaction than other places on my body. I went to a dermatologist, who gave me an injection and topical cream and I was back to normal quickly after.
You obviously need to communicate your allergies to providers. I'm sure they'll be understanding and cooperative. Good luck!