Cracking of the fingertips may be an allergy. I suggest that you consult a dermatologist about possible allergy (patch) testing, as well as topical cortisone cream treatment. Stress may make such a rash worse, but doesn't cause it. As to the smell, upset stomach, cracked lip, and itchy neck, I have no idea what connection these might have with the fingers.
Take care.
Dr. Rockoff