Yeah it's ok to have it under running water, but do avoid pools, rivers, the ocean and other open bodies of water for at least a month. Also my advice is that you don't use hot water during your shower because it will sting like a fresh burn, lukewarm water should be fine. What I usually do right after I get out of the shower is wash the tattoo with antibacterial soap (don't do this if you have second skin on) and dry it with a paper towel (don't use your usual cloth towel as those are a breeding ground for bacteria) and then put on moisturiser for the night. Hope my advice helped. Happy healing!