No, there is no way to get your tama back after it dies. You'll just have to wait for a new one. If it helps, you can look in the family section of your tama, then go under History. You will be able to see your past tamas. It can only hold about five tamas though, so you may not see all of them. Don't worry, most of my tamas only lived for about five or six years, don't feel bad.