"I am going to the doctor."
Translation:Ich gehe zum Arzt.
"zum" is short for "zu dem", where "dem" is the masculine dative definite article. Ärztin is feminine, and the dative feminine definite article is "der", so it would have to be "zu der", which can be contracted to "zur".
Also watch that it is Ärztin not Ärtzin (z before t).