Sorry about the break up.
I have rejected someone and has also been rejected, but, while painful (and extremely awkward when i see these girls again) i can tell you that there are cases that rejection is for the best of both parts. Some people just don`t work well together as a couple. They may get along, feel atracted, but due to lifestyle and relationship expectations, will not work out because their paths are incompatible.
If a person values gender roles too much and the other don`t care about that at all, that kind of relationship is doomed to fail.
Of course you can, and you will. Take this time to rediscover yourself, vent with people you trust if you need to, and appreciate your own qualities. We all have strenght and weaknesses. We can hone our strenghts and work on our flaws, you can use this as a chance to become better and stronger. Not for another guy, but for yourself.
Relationships take time and work, if you eventually go for a new one, make sure the person is worth the effort and is compatible with your lifestyle and carreer.