SENSITIVE
thin-skinned
easily upset or hurt; sensitive.You'll have to handle Mary's mother carefully. She's very thin-skinned.Jane weeps easily when people tease her. She's too thin-skinned.
touch a sore spot and touch a sore point
to refer to a sensitive matter that will upset someone.I seem to have touched a sore spot. I'm sorry. I didn't mean to upset you.When you talk to him, avoid talking about money. It's best not to touch a sore point if possible.