I used to have a habit of drawing on my skin with ink and markers and started doing so at age 3 and my mom would tell me to stop it.
But she only told me to stop writing on myself because she had to give me a bath and get it off before we went anywhere.
I never got sick from writing and drawing on my own skin with ink or markers and the small amount of ink that gets on your skin from drawing on yourself is not gonna harm you.
It's much safer to write or draw on your skin using an ink pen instead of getting an actual tattoo that is permanent.
I wouldn't worry about it as you're not gonna get skin cancer or any other health issues from the small amount of ink.