Wikipedia has more on Phobophobia
Phobophobia (from Greek phóbos, "fear") is the fear of fears or phobias, or the fear that you’ll obtain one. People with this phobia are afraid of developing a phobia, leading to a self-replicating cycle, ultimately resulting in escalating circular fears. Some people with phobophobia already have one or more existing phobias, while others never had one but are afraid to develop one. Phobophobia is often linked to other anxiety disorders, such as generalized anxiety disorder, obsessive-compulsive disorder, anticipatory anxiety, hypochondriasis, nosophobia, medical student's disease, cyberchondria. Phobophobia is sometimes linked to fear of mental illness.
Phobophobia is one of the only fears that can directly lead to a feared outcome. Sufferers would limit activities to minimize their fears but it can lead to agoraphobia while getting involved in specific objects or situations can lead to phobias of those.
Symptoms of phobophobia include dry mouth, uncontrollable sweating, trembling or shaking, rapid heart rate and shortness of breath, crying, screaming or other hysterical behavior, trying to flee. Anxiety and panic attacks are the most common symptoms. Other symptoms include thoughts about death or dying, dread, and terror.
Phobophobia typically respond well to treatments like cognitive-behavioral therapy and hypnosis, but since it is often link to other anxiety disorders, it is important to simultaneously treat them all.