Hi chosen25,
Sorry you are having difficulties here. May I ask you a question? Why is it hard to accept the fact that maybe she really does just want some time to herself? I think that by talking yourself into believing that she's not interested in you is very self-defeating. If she apologized over and over again, it sounds to me like she cares about your feelings and is truly sorry for putting you off. It's possible she needs time to regroup from her breakup and to heal and recover.
Jumping into another relationship with someone after a break-up is not usually conducive to having a good relationship. It's called rebounding and it generally fails.
If you are pushing her to talk to you when she is not at all ready to talk, then you are most definitely pushing her away. You are not showing her that you have patience and understanding of HER feelings right now. I believe she showed you she cares about your feelings by the multiple texts saying she was sorry.
Please give her the benefit of the doubt before getting more angry over this. Take her words at face value until you have concrete proof that they are not true. I think you are jumping to conclusions possibly because rejection is difficult to take.....and you are feeling the need to protect yourself.
Sending you calming thoughts and wishes of peace.

sabby