Generally rearing is a result of confusion...
To back up, you need to ask for movement with the body, and put in place a 'block' with the hands/reins. Generally, if a horse won't back up, the rider will increase both the movement cue and the block cue... And if they aren't in correct balance, the horse has nowhere to go but up. they are simply trying to figure out what you want, and in their mind, up is a reasonable option.
Can you back her on the ground WITHOUT touching her head? Try using pressure on her chest. Everything we do with horses revolves around moving off pressure, so it shouldn't be too hard.
It sounds like she has associated a block on her head with 'up'.
Your movement cue and your blocking cue may also be out of balance... To me a cluck means forward, so that may be confusing her. Try just using your seat and your block (not a pull).