I agree with anxiousmom, you should know where your relationship stands. But it sounds like this girl is still getting over her cheating ex. She may be keeping the door open so that IF you did cheat/hurt/leave her, she can tell herself it was never that serious anyway. It sounds like she's afraid of getting hurt again, and you're carrying this burden. Just based on what you've posted, you might try talking to her about her trust issues, tell her you're serious about her, and need her to work on these issues for your relationship to have a real chance. She might not like to hear it (no one wants to admit when bad experiences are still controlling them), but until she can learn to let you in and love again, your relationship with her is always going to feel at arm's length. I hope this was helpful - good luck!
You absolutely have the right to ask her to define the relationship, it is your life and she is being unfair. Perhaps she is truly not ready to commit to you.