Although lawyer and attorney do have distinct meanings, the two terms are commonly used interchangeably. The label lawyer is applied to attorneys, counselors, solicitors, barristers, and advocates, while the term attorney carries the general sense of "one who is legally appointed by another to transact business for him." The confusion arises from attorney's more specific meaning: "a legal agent qualified to act for suitors and defendants in legal proceedings."
Now that we've untangled that legal web, let's examine the place of the courtesy title esquire. We don't know that its frequency has increased, but we do know the abbreviation often follows attorneys' names in correspondence and in formal listings, and less often follows the names of other professionals. We don't see any problem applying esquire to oneself, but some folks object to its being applied to women—a usage considered perfectly standard.
But before you append Esq. to a person's name, be sure of one thing: that the name is not already preceded by a courtesy title or honorific or already succeeded by a degree or professional rating.