First of all, I have to correct one thing you said about having to give your girlfriend unconditional love. Adult love relationships actually aren't and shouldn't be about unconditional love. The only relationship on earth that is supposed to be unconditional is the relationship between a parent and a young child.
Adult love relationships can't be unconditional. What if your girlfriend abuses you mentally or physically? What if she cheats on you? Are you supposed to love her unconditionally no matter what? Of course not! Now, let's discuss your plan about being friends in the hope that she'll come around.
There are two possible scenarios that I can imagine happening. In the first scenario, we can assume that she freaked because you became too intimate too soon. If that 's true, being friends for a while could help her to become intimate with you in a more gradual way. This would be like entering the shallow end of a pool, waiting until your body becomes used to the temperature, and then gradually moving into the deep end.
The second possible scenario is less optimistic. If she is terrified of intimacy, then your backing off and giving her time won't help. Time never resolves emotional problems. In fact, problems often worsen over time! Nor will diluting the relationship by being friends solve a problem like fear of intimacy. If anything being friends would only mask the problem and if she is truly terrified of intimacy she will run like a rabbit as soon as you try to get closer to her.
What you might consider is testing out the first theory in the hope that she just became frightened because you guys just went too fast. Be friends and see if she is gradually able to become more and more intimate with you. If so, then the plan worked. If, on the contrary, the friendship plan doesn't bring her closer to you, then your next move would be to talk to her about her fear of intimacy. In this case, you would want to encourage her to talk about her childhood, who hurt her, who let her down or abandoned her?
Another possible cause of a fear of intimacy is having been smothered or controlled as a child, so you'll want to explore this too. If you can get her talking about the problem, you will be on the path to healing the fear. Let me know what happens.