Sheepishness is the characteristic of being embarrassed or ashamed. A new teacher's sheepishness might make it hard for him to stand up and speak in front of his class.
Your sheepishness might be part of your personality — some shy people seem to exude sheepishness. On the other hand, sheepishness can come from a feeling of shame over some specific incident. Your dog's sheepishness might alert you to the fact that she's chewed up your new boots, for example. The noun sheepishness comes from the adjective sheepish, which in the 1200s simply meant "resembling a sheep." By the late 1600s, though, it came to mean "bashful or awkward among strangers."