My 8 year old daughter has multiple, tightly packed clusters of itchy, slight red, non fluid filled bumps on her elbows, knees, ankles, toes, and back of her hands.

Atopic Dermatitis? Your description is very suggestive of Atopic Dermatitis or Eczema. This condition tends to worsen with changes in weather, humidity, use of strong detergents or harsh body soap. Sometimes it may get super infected with bacteria or fungus. If moisturizers don't improve rapidly the condition, I suggest to see a doctor.