Medieval STI treatment, like many medical practices during the medieval era, was a lot of guesswork. In the days of the Black Death, people had only a rudimentary understanding of how illness worked, and STIs were so tied in with moral issues that it was difficult to talk about them in objective terms.
This didn't stop the cavalcade of medieval sex — it was thriving in all walks of life, with kings and commoners alike turning to "ladies of the night" for satisfaction.
The history of STIs is difficult to trace because it was taboo to discuss it. In the case of the medieval era, literacy was rare and most accounts modern scholars have access to come from physicians and clergy members rather than from the "workers" themselves.
We may never know all the facts about how people of the medieval era treated, dealt with, and prevented STIs, but what we do know suggests that — despite the lack of medical knowledge — it was of interest to them.
Modern researchers can make guesses about what STIs people of the medieval era experienced, but it's important to note they did not use the same terminology we do today. We can assume that syphilis and gonorrhea existed in the medieval ages, but they weren't known by those names.
"Burning sickness" may have been gonorrhea, but we have no way of knowing if every case was actually gonorrhea, or if other infections were also called that.
Though medieval people likely didn't have to worry about moderns sicknesses like HIV, we can't be sure exactly what illnesses they were concerned with except for those that were extensively covered, such as syphilis.
Without a solid foundation for what caused diseases, medieval people had to come up with their own theories about how illnesses spread.
For people who contracted STIs and were known to frequent "late-night establishments," some might suppose that any sicknesses they had were caused not by physical contact, but by sin. The act was sinful, but if it was for work, it was tolerated to avoid greater evils.
Despite this, sinning had consequences, and many believed fornication led to physical punishments we now think of as STIs.
Because medieval Europe was a patriarchal Christian society, women were seen as weaker and inferior to men. They were often considered temptresses, drawn from the concept of Original Sin from the bible.
This meant working girls were not treated with respect, especially when it came to STIs. By the logic of the time period, they might have engage with a leper, then transmit that disease to whomever they met with next, even if they weren't showing symptoms.
Women were more likely to be mentioned as carriers of disease and could be banished from stews (or bath houses) for carrying "burning sickness." When a man contracted a disease, he might blame relations with women — not with a single woman who might carry disease, but the entire gender — and instead turn to engaging with men to avoid future contraction.
Women were thought to be carriers and punished for it, despite the men they contracted the STIs from.
Much of what modern people know of this profession in the middle ages isn't based on first-hand accounts. Most of the population was illiterate. Education was primarily handled by the church, which meant the majority of people who could read or write were part of the clergy.
Given how it was considered a necessary evil but still inherently sinful, many historical accounts from this era are limited. Those that exist are likely tinged with anti-opinions since these writings likely originated in the church.