After two weeks it's not likely an allergy. It's also sort of slow for an infection. You should see an infectious reaction to a wound within 48 hours but it may not have been visible because of the ink. An infection would cause the Tat scars to heal more slowly than expected and would normally make the skin around the tattoo uncomfortably warm. It's possible something got into the Tattoo while it was healing.
If nothing else to protect your tattoo you want to have someone that can see this rash evaluate what's going on. Start by going to the tattoo parlor. They are going to be your best source for information about what an infection from tat work looks like, they have a lot of knowledge about treating bad tattoo reactions and they are responsible for your health in regards to the work they did.
If you are at all unsatisfied or unconfident with the advice you get from the tattoo artist don't hesitate to see a doctor. Fungal or Bacterial infections can do much much worse than mess up your tattoo. Take this rash seriously.