Formally, 我的狗 is correct. If you want to say you have more than one dog, just add number in front of the dog. For example, 我有三条狗。
Or, you can say "我的狗狗们", it is a cute way to say "my dogs", the tone sounds like "my doggies".
"Make" can be translated into many words in different context. In this specific context, you can translate it into "令","让", or"使".
Music MAKES you happy.