Huh. I tend to interpret "deep feelings that one feel like they shouldn't share", to be feelings that are heavy for others to hear and risk affecting them negatively/emotionally in turn. Like depression, shame, disgust, suicidal ideation, anxiousness, hopelessness, anger or betrayal. People might not want to share for fear of illiciting sadness, pity, shame, worry, or withdrawal in the listener.
What different associations we have learned to make.
I think there are different words depending on WHY you think you shouldn't share your inner thoughts and feelings.