Don't want to give up

My LDR girlfriend and I broke up about two weeks ago. A number of issues have been brought up and she keeps hopping around to different ones. We hit a bit of a rough spot and she started developing feelings for a mutual friend. We were together 10 months and it was the best relationship I've ever had. She said she needed time to think and breathe. We were talking about moving in together. I don't want to give up hope that something good could come of this. She says she still loves me and she misses me. If she didn't feel something she wouldn't keep bringing up issues right? She wants to keep me in her life. Is time really the answer? Everything is so hard and confusing lately. Most days I walk around in a fog and every other thing reminds me of her. I imagined a life together and I don't want to give that up. It's so hard to deal with all this.