No you should not immediatly start to date because that shsows lack of confedince and that you are desperate and need someone in your life to take out all the stress of your life but it is not showing affection to that person.
Yes, dating is FUN! ... And I do mean DATING in the literal sense of the word, going out on dates, but not going *steady* with any one person. Going straight into another relationship is a recipe for another heartbreak. Dating around leads you to the right person and the journey is just as much fun as the destination.