What are the possible complications due to hives?

Not much. There are usually not many complications from hives outside of the psychological distress.
Infection. Hives from an allergic reaction or medication can itch a lot, and all that scratching can break down the skin and allow nasty bugs to cause an infection. Also, hives may be a precursor to a more severe allergic reaction, one that could interfere with breathing and be life threatening. If you think you might be having an allergic reaction and there's rapid swelling of throat/mouth - time for 911!