Which of the following are signs of an allergic reaction to nail products?

Itching around the application area is a significant sign of an allergic reaction to nail products. Allergic reactions can occur when the immune system recognizes certain substances in the products as harmful, leading to symptoms such as redness, itching, swelling, or inflammation in the affected area. This hypersensitivity can manifest shortly after application or may develop over time with repeated exposure.

Other options like dryness and cracking of nails might indicate other issues, such as overuse of nail products or environmental factors, but they are not specific indicators of an allergic reaction. Similarly, strong nail growth does not correlate with an allergic reaction; it is often a sign of healthy nail conditions. Brightly colored nails are merely a cosmetic effect of nail polish and do not reflect any physiological response to allergens. Therefore, the presence of itching is the most valid indicator of an allergic reaction among the given choices.