No those are your thoughts, Paul says He finds a law in verse 21.
He says that this law is ANOTHER law in verse 23 and that this law is that when he would do Good, evil is present with him. He says that He delights after the Law of God after (down in) the inner man, but this other law that he finds wars against the Law in his mind. He then begins to call this other Law, the law of sin in verse 23 and says he is in captivity to it. It has become part of him, it is in his members. Remember Our Savior's words in
John 8:34? He said "He that committeth sin is a servant to it." Paul in recognizing this then cries out, "O wretched man that I am! who shall deliver me from the body of this death?"
So we now have two things. We have the other law, the law of sin warring against the Law of God in His mind. And due to the captivity, the fact that we have no way of escape in and of ourselves we have the end result which is death. For the wages of sin is death, as was said earlier in chapter 6 verse 23.
Then he makes a contrast between these to Laws. He thanks God that in His mind he is serving the Law of God, but sadly with his flesh the other law that he found, the law of sin which he is captivity to. For he that commits sin becomes a slave to it and suffers the end result which is death.
Rom 7:21 I find then a law, that, when I would do good, evil is present with me.
Rom 7:22 For I delight in the law of God after the inward man:
Rom 7:23 But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members.
Rom 7:24 O wretched man that I am! who shall deliver me from the body of this death?
Rom 7:25 I thank God through Jesus Christ our Lord. So then with the mind I myself serve the law of God; but with the flesh the law of sin.