Got a new tattoo, want to make sure I'm doing the right thing?

Hey folks! i got my 1st tattoo on Sat, it looked beautiful. Its starting to peel and whatnot and I just want to make sure I'm doing this right. In the mornings, I gently wash it with mild soap and water and let it air dry. Then I put some lotion on it (no additives) and go to work. During the day, I wash my hands and put more lotion on if it seems to look dry. I only used the antibiotic ointment for a day or two because my skin puffed up and it looked nasty. I also use a mary kay product on it that keeps it smooth and doesnt itch. I'm not picking at it, but it is peeling and scabbed a little. This is okay right? I'm I doing all right?