How can I reduce itching and swelling due to hives?

Hives. Remove the causative stimulating agent, if known. Try topical Benadryl (diphenhydramine) or Hydrocortisone and strongly consider addind oral antihistamines into the mix. I tend to treat with higher doses than once daily since skin oftentimes requires higher doses, but start with one and ask your doctor about dosing options.
Antihistamine. The combination treatment, sedating and nonsedating antihistamines, e, g, Atarax (hydroxyzine) plus zyrtec, works well. Known trigger should be avoided as well.