Mathematica 10.1, 46 bytes
LetterQ@#&&#==ToCamelCase@#&&StringLength@#>1&
Uses one less byte than the standard regex solution. It does three checks. LetterQ@#
ensures that the string is entirely composed of letters, and StringLength@#>1
invalidates single-letter strings. #==ToCamelCase@#
makes less sense, however. ToCamelCase
is an undocumented function I found that takes an input string AndOutputsItLikeThis. Since there is only one word, it will capitalize the first letter, so we check if the string is equal to that.