In The Screwtape Letters Lewis warns against Christian using the phrase "My God" in the wrong way. In one of his letters Screwtape informs his nephew Wormwood that he should try to make the phrases "My dog," and "My shoes," synonymous to the phrase "My God." Of course in doing so Lewis warns against this. If we think of "Our God" in the same way as our personal belongings then we will have totally the wrong view of God's sovereignty over us. We will begin to think that God is at our beck-and-call, ready to give us the things we pray to Him for, ready to smite all our enemies whenever they get annoying, ready to send His son for our sins etcetera, etcetera ad nauseum.
The phrase "My God" is not even, for us Americans, like the phrase "My country." As Americans we view our country as something that is ours, that we own, invest in, and have freedoms in. This might be the correct way to think of a country (Maybe. I'm not getting into that political discussion), but it's still not the way to think of "Our God."
The phrase that is most synonymous to "My God"--in its correct usage-- is "My King." If I had a king, I would be on his side, and he would be on mine, but he would be the one totally in control of me. I have no say in what he does, and my life basically belongs to him. I would live for him and serve him, and he would be mine, but not mine. The real meaning of this phrase says that "I AM HIS."
"Then saith he to Thomas, Reach hither thy finger, and behold my hands; and reach hither thy hand, and thrust it into my side: and be not faithless, but believing. And Thomas answered and said unto him, My LORD and my God."