So I tied my hair into my first ever ponytail today...

[Esper]

My hair keeps making bends at the ends that makes it asymmetrical. Like a curl, going into a wave. Basically the back of my head is the same as Silver's hair behind his head from GSC.

I can't use a straightener, so any ideas to make it more symmetrical?

A good stylist can cut your hair so it won't do that so much, but that's gonna cost you and it's still hit-or-miss whether you get a stylist who knows how to do it right. If the hair grows out its own weight will help keep it down. Just try to take care of it in the meantime. Brush and wash and all that. Putting product in - gel or whatever you like - can help it stay down, too.