If you send me the model i can help you

I think it's a weight painting problem !
some vertexs of the arm are also attached yo another bone elsewhere it can happen when you paint weights : sometimes you can by non attention paint over another bone.
But not sure , that's really strange.

(You can also delete the bone arms and recreate them
to see if thinsg go better ?)
If you can put your model on some host on the net , i'll download it and look at the problem.