So my main concern about my philosophical question is that is it a Ethic branch of philosophy? if not to which branch does it fit?
Since your question comes under the study of what is right and wrong in human behaviour or beliefs about what is morally correct or acceptable, this is an ethics related question.
Is it ever alright to share a secret?
Yes, but not all ... and not always.
You should not disclose secrets at inappropriate times.
If there is any harm to the world for not sharing a secret, it should be shared.
Just for an evidence: The world is still experiencing the consequences of hiding certain secrets (eg. secrets of harmful medicines). Think of the billions of innocent people in the history who sacrificed their lives for this reason!
The secret can be of someone else's or yours. You should think wisely while sharing others' secrets than of yours'. Don't share them if it is not essential.
You will get more instances from your daily life also. Just imagine what happens if you don't share your secrets especially with your doctor, lawyer etc.