Quick thoughts to have if you have trouble in your relationship : Do I know what really is the ultimate cause of my misery ( you being unable to be extrovert or her being one ) ?
Have I talk about it with her ( most important to do so if you struggle alone don't be in a relationship at all )
Have we both made efforts to appreciate each other lifestyle ? Are you two BOTH making an effort to go out of one's own confort zone ? THAT is to me the less obvious because people never understand that you could learn a lot from trying more to fit in with the other significant, and same for the other trying to fit in with you, both persons learns in a healthy relationship. Both persons need to be accepted and to accept not just by suffering from it but by embracing the other's trait that make you uncomfortable in the first place it'll help a lot and you'll understand more personnaly their point of view.
You will never really find someone that is " compatible and perfect for you " this simply is disney or teen drama relationship, A relationship is something you put some effort into if you ever want it to last, and I mean last so marriage etc not just some teen love; it's different if you know deep down you don't want the person for a lifetime.
Anyway lastly if you two did all those things ( comucication, personal efforts toward the other point of view and self reflect ) and still think you'll be less miserable alone ask yourself a last question : would my misery from a life alone and possibly heartbreak be worse than the hurt you are feeling right now ?
Lot's of love to you, hoping you'll both be happy.