The ingredients contained in Sharpie markers are considered safe for most peoples skin and there's usually no harm in writing on yourself using Sharpie or other markers.
However some people may have a skin allergy to the Sharpie ingredients and sometimes the Sharpie could cause a person to get a rash on their skin.
But most times it's perfectly fine to write on your skin with Sharpie and no health issues will come out of it unless you're allergic to the ingredients however.
I've written on my hands and arms before with Sharpie and never have I got any bad skin reactions or any other health issues as a result.
Even inhaling a Sharpie smell will not harm you because it's deemed safe.