Touchier

adjective

1. (of a situation) Extremely sensitive or volatile; easily disturbed to the point of becoming unstable; requiring caution or tactfulness.

   "It is an extremely touchy situation, with everybody's patience wearing thin."

2. (of a person) Easily offended; oversensitive; ticklish.

   "He can be very touchy when you talk about his cat, so be as tactful as possible."