"Today's generation of the Cottrell family bears a name that was brought to England by the wave of migration that was started by the Norman Conquest of 1066. Cottrell is a name for a "serf or bond tenant who held a cottage by service." The name is derived from the Old English "cote," which means "shelter," or "cottage."
Spelling variations include: Cotterell, Cotterel, Cotteral, Cotteril, Cotterill, Cottral, Cottrall, Cottrell, Cottrel, Coterall, Coterel, Coteril, Coterill, Cotrall, Cotrell, Cottrle, Cotral, Cotraul, Cotrelly and many more.
First found in Derbyshire where they were seated from very early times and were granted lands by Duke William of Normandy, their liege Lord, for their distinguished assistance at the Battle of Hastings in 1066 A.D.
Some of the first settlers of this name or some of its variants were: Edward Cotterell who settled in Virginia in 1635; John Cotterell settled in New England in 1655; Timothy Cotterill arrived in Boston in 1765; Edward Cotteral arrived in Pennsylvania in 1772."
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http://www.houseofnames.com/xq/asp.fc/qx/cottrell-family-crest.htm
Hope this helps!
EDIT: By the way, your family name's crest is at the link above.