Advice please. My girlfriend always flinches when I raise my hand up to hug her or grab hers

She'll actually cower a little before she realizes what is actually happening. 

Her past involves an abusive mother who broke her jaw and other parts and a big guy (prison record) re-broke it freshman year. Her boyfriend before me use to leave bruises and hurt her pretty bad and so she and him are done. 

I love her and it kills me when I scare her. I would never hurt her. 

How can I change this?

(I'm 17 and she's 16 until late June)