Arabs are a very sensitive/spirited breed in general, which I love about them! It does make learning to "take a chill pill" something that usually - has - to be taught, unlike some other, more naturally relaxed breeds.
edit: just re-read and notice that you have in the round pen! anywhoo
Have you tried lunging her at all? (especially if she's in a small paddock/stall most of the day?)
Something fun to try while you're lunging, is to desensitize her to objects hanging from her saddle/touching her sides. Things that will be safe if they fall off -- a plastic bag tied to the horn/stirrup, or an old plastic water bottle with a few small rocks bouncing around inside it. These are great to start off with, and will help her to learn that not everything new on her back (like people - even though you aren't "new" exactly, but new within the past 24 hours. xD) needs to be reacted to. It doesn't seem as if she's scared or afraid of your leg/you - just overreacting to it, typical of young ones! (: if she does well with a plastic bag and rock bottle, try an old bedsheet or "cape" like object, just something light that flows (but always keep it away from her legs - and make sure it's flimsy enough she can tear it up rather than break a neck if she does happen to step on it!)
Once she's great at ignoring light objects, try heavier ones! I've used bailing twine tied to the buckles near the horn of my saddle to hold things like a very small, but still weighty, tire from an old kid's bike, something that has a little impact (but obviously doesn't tear up/bruise them!) to simulate your leg. From there, it's easy to switch to intentionally bouncing your legs'/heels on her sides rhythmically while walking, trotting, and even loping! It doesn't sound like you'll be able to over-do it and make her "dead-sided" (believe me, it takes way more than that to make them dull. Horses are way too smart!)
Does she collect/give her face to you at all while under saddle? That is also a good place to start when trying to teach "good" pressure. If you can teach her to flex to both sides, and put her head down when asked (good to practice for bridling/haltering too lol) it's great to transfer those things into saddle.
Another thing (I'm so sorry this is so lengthy already lol) is, if it's forward motion she's being overly sensitive to, to practice using your legs in a way that doesn't mean "go forward." For instance, things like pivoting on the fore and hindquarters uses leg, but doesn't mean "speed up." Also, teaching her to side pass is incredibly useful and will help soften her reaction to her sides. And again, it's best to teach these things on the ground first (youtube videos of showmanship are a nice visual of #goals lol) before the saddle. And when you get to where she's good at pivots/sidepassing under saddle, you can move on to more forward things like leg-yields super easily!
I hope this helped, but definitely don't feel obligated to try anything you don't feel safe about/ready for.