You say she will "randomly" go up. I doubt that. Usually there is a trigger, although you may not recognize it. Your goal is to learn what the trigger is. Something you do? Something in the environment? Something that moves/shifts on tack or clothing?
You also need to learn to feel the rear BEFORE it happens. I have a horse that will rear, but when I am on her I am ALWAYS attentive for it. If I feel her ready for a rear, I immediately change her direction or push her forwards, depending on the situation. In months and months now she hasn't managed to get up even a few inches. However, I won't let anyone else ride her (except MDH who stubbornly insists he can handle her... <sigh>); she is just too unpredictable.
If you are not experienced in training, you may indeed want to look for help from a trainer. In my case, I don't have trainers available and have spent many stupid years learning stuff on my own. Not something I would advise to others.