It’s so frustrating that people still bully their peers and throw around the word fat. You heard it once and it had this profound of an impact on your well-being, which is a normal reaction. I wish people were more sensitive and realized the damage they could be doing.
But that aside, you’re not fat. Your height and weight seem normal and if your doctor says that it’s a good weight, trust them. Starting yourself and obsessing over calories will just drive you crazy. Please, try to forget what one rude person said to you and focus on all of the compliments/good things you hear about yourself. It’s not fair to let one negative comment have more of an influence than a million positive comments, especially because the positive are said out of love and friendship and the negative was out of disrespect.