It's always best to avoid soaking new tattoos in water - at least for the first two weeks, as the skin has been damaged and is much more likely to get infected or irritated by particles, either chemical or biological, in the water.
Having a shower isn't generally considered harmful to a new tattoo, as long as you don't scrub the tattoo whilst in the shower. Be sure to clean it very carefully at first so you don't damage your skin. When it comes to swimming, chlorine can cause problems in the beginning so, even after the first two weeks, limit your exposure to chlorine-treated swimming pools. Some people suggest that it's best to wait for a long as three months before you can really stop worrying about getting your tattoo soaked. This is because it can take that long for a new protective layer of skin to form over your new tattoo, protecting it from chemicals and bacteria. Lots of people get tattoos in summer, or just before, but, in reality, this is probably the worst time to get a new tattoo, especially if you're a fan of the outdoors or swimming, as both water and sun exposure can harm your tattoo. If you're a fan of the summer, it's worth getting your new tattoo a few months before the sun and heat really get going to allow it to New Tattoo Healing Times fully.
Underwater tattoo (source)
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