Condoms are provided by brothels to protect the girls from YOU, not to protect you from them. They aren't likely to use any product that will put them in danger of getting a disease from you. If it's a major concern, ask the brothel or bring your own condom.
Condoms that are used in such places are made up of latex and it is an efficient barrier to HIV if they don't fail.
Your fear is irrational. You weren't at risk.