Need some advice about my tattoo if my first one.

[Blue]

it looks okay, don't pull the peeling off, let it come off on it's own. If it does mess up the design, the artist can fix any tiny flaws after it's healed but, I think as long as you take care of it like the artist told you, it will be fine.

Remember the ink is in several layers of your skin so, if one layer peels it won't hurt the tattoo. Once healed you can sun burn them and it's okay as far as the look goes. Of course they do fade over the years, but they never disappear.