Why would the outer of the vagina hurt during and after sex?

Several reasons. First, make sure there are no sores, ulcerations or small tears in that area. Any lesion should be checked. If the vagina also is dry during sex due to lack of lubrication, that will cause discomfort due to the friction and irritation. Try additional lubricant and talk with your partner. Slower entry and movement in the vagina may help the canal adjust and cause less spasm as well. Communicate!