Hello I am a solicitor with 20 years experience. I will try to help you with this.
If, as is almost certainly the case, the owner of the dog has acted negligently or recklessly, in failing to control their dog leading to the fatal attack you describe then you may have an action against them. However it is unlikely that the courts would award much, if any compensation to you. The courts take a hard headed view about compensation for emotional trauma and upset and award very small amounts of damages. If you can prove worsening of a medical condition then you might have a more substantial claim. This would be difficult to prove however and you would need to pay for medical reports etc.
You have reported the matter to the police and if there is a prosecution and conviction then you can be awarded compensation as victim of crime by the sentencing court under The Powers of Criminal Courts Act. The best approach might be to keep in touch with the police so that yo know what is going on in the case and maybe to provide a victim impact statement to the police which can be taken into account at sentencing.
Thank you for your help