First of all, you should be a bit careful in who you talk to. Islamic or non-islamic, there should be very few people you should trust completely. We all have to learn what limits to set with whom.
Secondly, hopefully she didn't share your 'secrets' with anyone.
Third, no, don't feel bad and don't react because you don't know the circumstances why she chose to tell someone else about her engagement. Just because you confide in someone doesn't mean it's a two way street as much as you'd like it to be.
Now that you are aware of this person's nature, be careful in the future.
Hmm so you are saying that person is not trustworthy because as far I understand your post you are saying that its not necessary that she should tell me her secret.
Anyways I have to wait for her until she tells me about her engagement.But its a big thing and people knows about it.
Unfortunately the trust wasn't a completely two way street. I would talk to her, but don't take it too personally. She may just be a more personal/introverted/shy person.
May be but then why she wants to get everone's secrets?