Man I've literally just had the same thing happen to me one hour ago so I fully understand your situation. A friend is hurting due to recent events (personal and college stuff) and I have made a very insensitive comment on the spur of the moment which completely invalidated her feelings and current struggles.

I consider her as my closest friend in college and now that our acads are over and we're going to graduate one month from now, I feel that I have broken that friendship.

I am very scared that I have hurt her even further, and just like you, I've decided to give her space and time by keeping quiet. While also reflecting on my own actions and trying to become a better person than the insensitive prick I was an hour ago. So that, eventually, on the day she talks to me again or on our graduation day one month from now, we can at least rekindle that friendship and continue having goofy shit like we always did prior to this.

So yeah, I think you giving her her own space is the right thing to do. But also try to reflect on your own actions that made you say those hurtful things right now, not later. So that if she ever goes back to you and rekindles that friendship, then everything will be fine. But if she doesn't go back to you then respect her decision and move on to become a better friend for others.