It is possible that the red bumps on your arms are due to an allergic reaction, especially if you have never experienced this type of reaction before. If the bumps do not go away after 7 days or if you experience other symptoms such as fever, difficulty breathing, or palpitations, it is recommended to consult a doctor. In the meantime, you can try applying cool, damp compresses or using calamine lotion to help relieve any itching. Remember to keep the affected area clean and moisturized with a fragrance-free lotion once the skin has healed.