In the past a few days I have developed some bumps on both of my hands. Some of them are itchy. What are they? How do I treat them?

Dyshidrotic eczema. Use an otc antihistamin such as claritin or benadryl (diphenhydramine) to reduce ithching. Apply otc corizone cream to the hands. If does not get any better see doctor. Check this link.