What is the term which can be used to describe a person who is suffering from many phobias? I searched about this on Google but found nothing useful.
The condition is called polyphobia:
An abnormal fear of many things; a condition marked by the presence of many phobias.
The person suffering from polyphobia is polyphobic:
Many phobic individuals have more than one phobia and hence are polyphobic.
A person suffering from a number of phobias.
'Fraidy-cat is more colloquial. It refers to a very fearful person, afraid of everything, easily startled.
http://idioms.thefreedictionary.com/fraidy+cat - also as suggested here, you might use coward.
Phobophobia can also be defined as the fear of phobias or fear of developing a phobia. Phobophobia is related to anxiety disorders and panic attacks directly linked to other types of phobias, such as agoraphobia.