The only STD that can present with burning of the skin of the scrotum would be genital herpes. Genital herpes can cause sores or other symptoms anywhere on the genitals. The sores of genital herpes occur much more often on the penis or around the base of the penis, but the scrotum is also possible. In any location, herpes can cause some burning for a day or two before the onset of sores of the skin. It is not a common presentation to have burning of the scrotal skin, so this should not be a major worry, but it is the only STD that can present with this symptom.
However, there are conditions other than STDs that can cause burning of the skin of the scrotum, most often a sensitivity to a substance to which the skin has come in contact.
Burning deeper in the scrotum can occur with an infection of the testicle or the tube that drains the testicle (the epididymis), but if there is no tenderness, this is less of a concern. Redness around the urethral opening can also be due to an infection of the urethra, but there would typically be some burning in that area, either with or without urination.
So, from the perspective of an STD, the primary concern is whether any sores develop over the next day or two to suggest the development of herpes. If any sores develop, then you should be seen quickly. There is no medicine that can completely stop a herpes infection, but there is a medicine that can shorten the duration of infection, and it works better when started as soon as any sores develop.
In the interim, it would be OK to take an oral antihistamine, which can help if the burning of the skin is a reaction to something to which the skin has come in contact. Any of the over the counter antihistamines would be fine.
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