Where are you getting this "old ink mixing with new ink" thing from? Ink put under the skin doesn't "mix." If you put white ink in the same place as you have red ink, it doesn't turn pink. That's not how tattooing works. The simple explanation is most likely the correct one. It's not likely allergies, it's not after care, it's not ink mixing, it's just a heavy hand. Allergies don't just go away. If you were really allergic to the ink, it wouldn't just heal. That's not how allergies work.
I understand you're looking for answers, but you already have the answer and now there's nothing to do but wait and see how it heals.