Dog Fight

First of all I live in an Apartment complex in Houston Texas. Last Sunday 4-27 My girlfriend was walking my dog who is a Boxer on a leash. While walking by my neighbor's apartment my neignbor asked my girlfriend to stop for a minute and answer some questions about a leak that is effecting both of our units. When my girlfriend stopped my neighbor yelled to his wife for them to put their dog back in the house as their dog ran outside their door, directly in front of my neihbors, Husband and wife.. At that point their dog quickly ran up to and jumped at my dog. Then My dog Bit their dog, and proceded to attack their dog, who was "at large" not on a leash. Their dog who was smaller than mine survived the attack, but surffered severe bodily damage resulting in a $1,600.00 vet bill. I did not witness the incident, but out of sadness for their family's hurt dog, I paid her $800.00 cash the evening of the incident to help cover their expense. The next day she came and asked me for more. Against my better judgment I gave her 200.00 additional dollars, and she said it was enough and she would leave me alone. Today she came to my door with a friend and told me that If i refused to pay the entire bill and accept 100% responsibility that she would take me to small claims court, and get it out of me, and would try to have me evicted from my apartment. I said no, as I am not sure if I cary any liability in this matter, much less 100% of the liability. In your professional opinion am I liable in any way, and if not should I counter sue as my girlfriend and her children were traumatizedand in shock, by the incident? Is a counter suit appropriate? No people were injured during this, But they beat the tar out of my dog.