Dear Reader, Certainly. Some people experience mild reactions when they use latex.
Reactions tend to worsen with time and exposure to latex.
On the other hand, there are people who are truly allergic to latex. Generally, reactions to latex in condoms tend to be less severe than reactions to latex in gloves. At the extreme, a person could experience difficulty breathing, and even go into anaphylactic shock. Severe latex allergies, however, are rare. If you wear latex gloves, presumably for work, you could speak with your boss or employer about what your alternatives are.