It's called agoraphobia, or being agoraphobic.
Using the japanese term while not being japanese just glamourizes the condition to otaku gaijin. Cut it out.
Actually those two terms are mutually exclusive, agoraphobia is "an abnormal fear of being in crowds, public places, or open areas, sometimes accompanied by anxiety attacks." whereas a hikkikomori is someone in a state of social withdrawal, the closest english word I suppose would be recluse or social deviant, but neither of those describe the cultural distinction of the "Hikkikomori", usually being young men who have family to take care of them or some other source of financial beneficiary.
Agoraphobia and hikikomori are similar, but really are entirely different conditions. Agoraphobia is an irrational fear, as all phobias are. Hikikomori is, upon extensive analyzation, frighteningly rational.