You have several claims that you can bring in a lawsuit against the owner of the pit bull. First, you can sue for negligent infliction of emotional distress. Second, you can sue for the loss of your dog (you can not receive pain & suffering, but you can receive compensation for the loss and medical bills). You may have other claims as well, but you definitely have a claim for Negligent Infliction of Emotional Distress and the loss of your dog.
You should consider contacting an attorney to assist you, as you may have a difficult time bringing a Negligent Infliction of Emotional Distress claim/law suit on your own. If you have any questions, feel free to contact me directly. You can obtain my contact information on my website at www.kregerthacker.com or on my avvo profile.
I see no mention in your facts or the initial response thereto about reporting the attack to the police and animal control. They should have been notified that same day. Do so now, if you have not already.
Document all your damages from this attack; vet bills, cremation/burial costs, if any, as well as what your investment in the deceased dog was (purchase costs, vet care prior to the attack, etc.).
Once you have documented and totaled your damages, you can send a demand letter by certified mail/return receipt to the owner, or have counsel handle the entire matter for you, if you so choose.
Your state and county bar associations can assist you in finding attorneys practicing animal and tort law.
You must report this to both the police and animal control immediately. You have claims for vet expenses and for replacement value of your dog. Unfortunately, the law considers animals as property and there is no claim for pain and suffering. You should also speak with a local attorney for further guidance. The North Carolina Bar Association can give you a referral: http://www.ncbar.org/