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Some peeling definitely is normal, including peeling color. I peeled more with my mermaid than I did with my quote.

The sunburn thing, that's one of the ways I described my first tattoo as well, so you're definitely not alone in that regard either!

Since you're saying there's no pain or swelling you're probably fine, although you can always call the artist to double check if the amount worries you, but peeling in general is definitely normal, including the color. Definitely continue washing and lotioning as per the artist's directions. If you're wearing clothing over it that may cause some rubbing as well, so if possible perhaps try to leave it uncovered, but if it's not possible that's understandable too. My first one was on my leg and I was working at the time so I'd have to wear pants, but I'd switch over to shorts after work so it wouldn't rub, and also because summer. But since it's cold out where you are it's understandable if you need to wear long sleeves.

That being said, definitely avoid picking it like you've been doing as well. Let it peel and fall off naturally and it should be fine!

Looking forward to seeing the finished product!