see How to get read data from response header in jquery/javascript for obtaining the response info.
Assuming you are using the AWS POST operation http://docs.aws.amazon.com/AmazonS3/latest/API/RESTObjectPOST.html
I suspect that the URI it returns is the one with amazon's domain: https://s3.amazonaws.com/Bucket/Object
if you are using a "web" bucket and want to use your custom domain you will have to figure that out for yourself. You already have the bucket name since you provided it in the call.
Another wrinkle could be the permissions of the file after upload. Be sure to set a policy on the paths for the uploads appropriately.