Referring to the data you provided (tiny clusters of raised itchy white bumps on hand and up the arms, popped two zit like bumps on each hip bone that do not heal after two weeks, environmental allergies to house dust, pollen) you might have experienced eczema. Eczema is a type of allergy which appears when the skin comes in direct contact with the allergen. Red, itchy areas appear with clusters of bumps. These bumps are usually red, while in your case you report them as white. This is what tells you to visit a dermatologist for a visual inspection. It is very hard to tell almost any change on the skin without seeing it. If eczema is confirmed, than antihistaminic medications and avoiding the contact with the suspected allergen are likely to be recommended.
The zit-like bumps might have been inflammation of the skin glands. If they were somehow infected then the healing process might have been delayed. The dermatologist might suggest applying local antibiotic creams to treat the infection and speed up the healing process.