Amethyst: sword-and-sorcery for the modern girl
This is from the limited series Amethyst for greenmask, who says she's never seen it. Dial-up unfriendly.
Amy Winston is a normal girl in the DCU who's coming home to open her birthday present from her parents. Unbeknownst to them, a lizard familiar has switched gifts.
Why does he carry a snake?
After being rescued from fantasy bad guys by fantasy good guys, Amy is told that she was born in this magical dimension called Gemworld. Good news is, she's a magical princess called Lady Amethyst and the cool necklace allows her to use magic! Bad news, her real parents were killed by the Big Bad Guy, Lord Dark Opal, so the Exposition Fairy, "Witchmother Citrine", hid her on Earth. The rapid aging is caused by the time differential between dimensions--everyone else remains the same age as they pass back and forth, but Amy/Amethyst goes back and forth.
They want her to lead the resistance since her parents used to rule Gemworld, but she begs to go home. Amy's half-convinced the first time was all a dream, but wants to go back later. Her dog jumps into her magic portal a second too late and gets stuck between dimensions. Amy gets kidnapped again (happens a lot in the first couple issues when she is still a noob) and the castle defenders are magically rooted. The witchmother hears the ghostly barking from between dimensions..
Gemworld is one of the places where all the fairy types went; so unicorns are more common than dogs. Then the dog rescues her. For serious.
The guy with the blue-lined skin is Lord Dark Opal.
She has good adoptive parents. Isn't that amazing?
The war heats up, killing some of Amy's followers and even spilling over to Earth. Amy says goodbye to her parents so she can save both worlds. She goes through intensive war training.