Saran wrap on a new tattoo after the first 2 hours of getting it is a no-no! And no, not every artist knows best!
Before you go to sleep, wash it, apply some ointment on it, and get a thick napkin that doesn't tear easily (Kleenex brand is great), and tape it over that area.
And as soon as you wake up, take it off, and wash your tattoo and re-apply the ointment.
The saran wrap doesn't allow the tattoo to breathe, and when sweat gets all built up under it, and sticks to your tattoo- it's not going to be pretty if something goes wrong!
Also, if he failed to tell you this, then I'd start following these directions as soon as you can. (And go to a different artist next time.)
For the first 3-5 days, you should be using Aquaphor, Tattoo Goo, or A&D ointment on it. Just enough to keep it moist until your next wash. And I recommend washing it with gold Dial soap... At least 3x a day. Pat it dry with a paper towel or clean wash cloth. Don't rub it.
After the 5 days or so, use a no aloe, non-scented, no healing lotion on it such as Lubriderm, Curel, or Neutrogena body lotion. (I was recommended the Neutrogena by my recent artist because my skin was sensitive and the lotion seems to have helped.) Use this for the next week or so.
You may notice that your tattoo will get funny looking and have colored flakes of skin falling off. Don't worry- your tattoo isn't coming off. This is just a normal part of the healing process. Do NOT pick at these flakes, let them fall off on their own.
If you do, you can pull color out of them and mess up your beautiful tattoo! I did that with my first tattoo... my bird is dark grey with black spots, instead of all black. :(
Best of luck!