Birds singing to you is a good sign in general. They give away inner peace, balance of spirit & mind. Sometimes we see things in our dreams that although not entirely true, are aiming to give said result. If you are in a bad emotional state, you can see a dream which reflects just that, but if you have a strong fighting spirit as i say, you could see a dream which aims to give the necessary "boost", to help you come back standing. Personally i think you need to see if there is a pattern in events concerning you. There is a good chance that the "singing bird" dream is giving away something specific. I know because i have reoccurring dreams, situations or people that have specific meanings for me.
By the way if you see caged birds it means that you are "securing" something, love, happiness,success. Even better when they are singing too. Lucky you.