How can you remove blotchy, red bumps from a fresh tattoo?

Steroids. This is may be a minor infection which may require antibiotics or an allergic reaction which may respond to topical or systemic steroids, if it persists the areas can be treated with a fractionated erbium laser to remove the problem ink.
Tatoo Reaction. From the symptoms any allergic reaction to the ink of the tattoo needs to be ruled out. Take some antihistaminic like Benadryl (diphenhydramine) or Claritin and apply some calamine lotion or mild steroid cream on the rash. If the symptoms are severe then please get it evaluated from a dermatologist as oral steroids may be needed. Also consult an allergist and get a patch testing done for the ink of the tattoo.