should I feel guilty about lying to my family

ab
--- I'm 22, living with super strict parents. After being cheated on I feel horrible about myself and I want to feel good again by working out. My family discourages this, bc they think I'm trying to go "anorexic." I've been wanting to go to the gym after university (I'm currently doing school full time & don't work) without them finding out.. but the only way to do this would be by lying to them.. should I feel guilty for this??