What would happen if, say, a young lad in 1200 AD England discovers that he just can’t wear the ubiquitous wool clothing without breaking out in a continuous nasty rash?
As you can imagine, skin conditions of all kinds have been known for about as long as we have any kinds of historical medical records--they're usually grossly apparent and often symptomatic. Contact dermatitis specifically (the technical name for this kind of allergy) has been known since ancient times, although the extent to which they were attributed to supernatural causes versus more pedestrian ones obviously varies a bit depending on the culture and the people writing. Hippocrates, in the 5th century BCE, did have some idea that there might be external physical causes of some skin conditions. By the 1st century CE, Pliny the Younger discusses that some people who worked with pine trees for a living got rashes on their hands from doing so. However, they didn't use the same classification system for diseases that we do, so it's not always straightforward to trace a line from the conditions that they describe to our modern ideas of disease.
About the only European source I know of discussing contact dermatitis specifically before the modern era dates from 1700 in Italy, with De Morbis Artificum Diatriba by Bernardino Ramazzini discussing occupational health hazards, including skin irritation in laundry workers.
A source: Smith, D.R. (2009), The continuing rise of contact dermatitis, Part 1: The academic discipline. Contact Dermatitis, 61: 189-193.