If you do not know how socialized this filly is, why don't you turn her out with the old alligators (that is what I call old mares). Nothing teaches a young horse how to have proper respect better than a couple of old alligators. Just turn her out during the day and put her up in the evening to eat. Horses are much easier to handle and teach when they are living in a herd situation. They learn manners the natural way. Then, they just have to learn to respect a person like they already respect the herd leader.
I think you are being way to easy on her. People just do not understand that they are doing no favors when they let a horse be aggressive like she is. They are not made of china and they do not break. They are always sorting out where they are in the herd pecking order. So every aggressive move toward a human herd member must be met with instant consequences. You cannot hesitate, because whatever you accept, is what you are teaching the horse to do. . Every single time you interact with a horse, you are training it --- if not to do something better, then it is learning to do something worse.
The one thing you do not want to do is be 'pecking' and 'nagging' at a horse. They hate it and they never learn to respect it. They just get ill tempered, lay their ears back and get more aggressive. You need to get after one hard for aggression and then leave them alone. You do not need to be petting and treating one or fussing with it. They are not dogs. They like you better if you keep your relationship more 'business-like' and efficient. Expect perfect manners, accept nothing less and then leave them alone.
I prefer spanking one hard for turning its butt. I do not mean tap or peck -- I mean spank hard. I only want to do it once so I want the horse to know it was the worst mistake of its life. Have you seen an old alligator mare take after a young one and run it off for a herd infraction? She does not just 'tap or peck' on one. They think they are going to die. That is what works best.
I do not hit them for trying to bite. I prefer to have a halter and lead on one when I am around it. So, I catch one first and then handle it if I think they may need some instruction. If one lays an ear back-- let alone bares its teeth -- I jerk the lead-rope hard 5 or 6 times. Then I take the horse out into the open and back it up roughly, make it move its shoulder over and away from me both directions, back it up some more and then stop and act like nothing at all has happened. I do not pet or play with them. I expect them to stand at attention and watch my every move. I 'smooch' every time I ask it to move back or over and reinforce it with a lead-rope. This way, I am conditioning the horse to move when I smooch. A respectful horse moves back or over when you take a step toward it and smooch. That is all the pressure you should have to put on a horse that has proper respect for its handler.
If I had to spank a horse to make it face me, then I take the end of a long lead-rope and flip and flop it all over the horse until it stands still and understands that the rope did not get them but that their behavior did. Then I back the horse up two or three more times.
If a horse tries nipping and fussing at me or the lead-rope, the perfect solution is to hold a nail in your hand with about an inch of it sticking out and let the horse run into it. I fixes nipping without making a game out of it or getting a horse to get head-shy and dodge your hand. As a matter of fact, it takes a pretty good while for me to get a horse over dodging every time I move my hand when someone has tried to stop it from nipping.
Good manners means that a horse stays out on the end of a lead-rope when you say "Whoa!". It only approaches you when you tug on the lead and smooch and 'invite' it into YOUR space. It moves back or away from you when you ask it to. It does not bring its head around and reach toward you when you stand next to it. It will stand still while you brush it, comb its tail, while you pick up its feet, give it a shot or while you throw a blanket on it. They just know that what you want to do is the way it is.
For some reason, when you get a horse well-mannered like this, they WANT to be your best friend. They will follow you anywhere at a respectful distance and are happy for any interaction you chose to have with them. They just know that they are not allowed to initiate contact with you --- just like they do not call the shots in a herd of alligators. A respectful horse is a happy horse. Their ears are up and 'working'. They acknowledge everything you say and do.
I know I am leaving a bunch out, but when you do it all of the time, it is just second nature. I cannot remember that last time I had a young horse try to nip me or had one lay an ear back at me. They all like me, come to me and wait for me to feed or catch them or ???? They are never afraid of me, but they sure don't mess with me.
Hope this helps.