What you may be dealing with is call sepration anxiety.
Getting a new dog may or may not help.. you may end up with two dogs in trouble not one. It may not stop the first dog from wanting you and it may not want a new dog. It maybe it just wants you only.
Radio is sometimes helpful if you tune it to a station you usually listen to or a classical station. you want normal and calm. Bad thing about radio is that dogs sometimes need quiet and sometimes they have those loud sounds that makes things worse so a CD with calm sounds like Through a dogs ear on a timer maybe more helpful.
For sepration anxiety building the dogs confidence is a must and working with it on training and being able to follow your requests and learning great tricks help. Dog needs to learn he can cope without you it not easy but it can be done.
As well as teaching settle.
Great little article on what it is and what to do to help.
Separation Anxiety | The Humane Society of the United States
In cases of very bad sepration anxeity drugs like cmposure or bio calm or even prozac can be given by a vet to help keep the dog calm through retraining which takes time and there is not quick fix to this.
JL