Could you post more of the song? It would be helpfull .
As for "fancy me" I think the singer is telling someoen to fancy her, to like her and take a romantic interest in her. The definition is highlighted in red below.
n. pl. fan·cies
1. The mental faculty through which whims, visions, and fantasies are summoned up; imagination, especially of a whimsical or fantastic nature. See Synonyms at imagination.
2. An image or a fantastic invention created by the mind.
3. A capricious notion; a whim.
4. A capricious liking or inclination.
5. Critical sensibility; taste.
6. Amorous or romantic attachment; love.
a. The enthusiasts or fans of a sport or pursuit considered as a group.
b. The sport or pursuit, such as boxing, engaging the interest of such a group.
adj. fan·ci·er, fan·ci·est
1. Highly decorated: a fancy hat.
2. Arising in the fancy; capricious.
3. Executed with skill; complex or intricate: the fancy footwork of a figure skater.
4. Of superior grade; fine: fancy preserves.
5. Excessive or exorbitant: paid a fancy price for the car.
6. Bred for unusual qualities or special points.
tr.v. fan·cied, fan·cy·ing, fan·cies
1. To visualize; imagine: "She tried to fancy what the flame of a candle looks like after the candle is blown out" Lewis Carroll.
2. To take a fancy to; like.
3. To suppose; guess.