My two dogs are fighting!

Question
I am 19 years old and leave at home with my parents.  I have a chiuahua/jack russel mix puppy that is now 11 months old.  i recieved her when she was 8 weeks and she has been through training classes.  About two weeks ago my brother moved in with his dog.  He was adopted so we are no quite sure what he is but we believe is is part lab part bull dog.  My brothers dog is also well behaved and went through puppy classes as well.  He is two weeks younger than my dog.  The problem we have with the dogs is them fighting over EVERYTHING!  toys, bones, people, food, and water!  at first we thought abby(my dog) was so defensive because it was "her" house and she has not had to share before but it has been about two weeks and it has not gotten better.  They bite each other and even though its not hard they still bite and growl.  Rocko(my brothers dog) usually instigates all the situations that end in fighting.  To stop the problem for the moment i take both of the dogs snouts and hold them close and say no bite about three times.  My questions are: why are they still biting and fighting, am i doing the right thing by holding their mouths closed, how can we stop this behavior right away?  Any suggestions would be great because it has been so hard on my entire family.  Thank you for all the help

Answer
Are you sure they are fighting and not playing? I would recommend that you consult a local behaviorist that can come to your home and observe their behavior and recommend a course of action. Without seeing exactly what is going on, I cannot give accurate advice.