No, we do not inherit sin. Sin is not a physical problem. It is a moral problem.
Romans 5 does NOT say that we inherit sin. It says that "sin entered the world through one man, and death spread to all men because all have sinned."
It does NOt say "Sin entered mankind through one man, and sin spread to all men because Adam sinned."
What it says is:
Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come. But not as the offense, so also is the free gift. For if through the offense of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. (Rom 5:14,15)
It says sin entered by one man and death by sin. It is also clear that even those who don't commit the sin of Adam are still under the curse. The Scriptures are clear that sin is an absence of righteousness and babies while innocent cannot be considered righteous in the Biblical sense. In the Old Testament and the ancient world if you were in debt the legal remedy could be casting you and your family into slavery in order to satisfy the debt. The issue is not one of offenses that occur but the lack of the means to satisfy the debt of sin. Paul makes it clear throughout the book of Romans that we are born in sin and that all are both aware of God's divine nature and that our conscience testifies against us that we are in fact sinners, whether by acts of commission or acts of omission.
James 1:14-15 says "But each person is tempted when he is lured and enticed by his own desire. Then desire when it has conceived gives birth to sin, and sin when it is fully grown brings forth death."
James is addressing issues in a church that has fallen into error. These people had already received the Word of God and been born of the Spirit:
James 1:21 "Wherefore lay apart all filthiness and superfluity of naughtiness, and receive with meekness the engrafted word, which is able to save your souls."
The temptations he is talking about are more like the weeds that grow up around the word and chock it out before it can bear fruit and quite possibly persecution.
Luke 8:11-15 "This is the meaning of the parable: The seed is the word of God. Those along the path are the ones who hear, and then the devil comes and takes away the word from their hearts, so that they may not believe and be saved. Those on the rock are the ones who receive the word with joy when they hear it, but they have no root. They believe for a while, but in the time of testing they fall away. The seed that fell among thorns stands for those who hear, but as they go on their way they are choked by life's worries, riches and pleasures, and they do not mature. But the seed on good soil stands for those with a noble and good heart, who hear the word, retain it, and by persevering produce a crop."
They had heard the Gospel and had received it but were in danger of having it choked out by carnality and persecution. Paul is addressing the same kind of mistreatment in his first letter to the Corinthians where the poor were deprived in the love feasts. Some would stuff themselves and even get drunk while others left hungry.
I Cor. 11:21 "For in eating every one taketh before other his own supper: and one is hungry, and another is drunken."
Paul says that they had failed to discern the body of Christ and for that:
I Cor 11:30 "For this cause many are weak and sickly among you, and many sleep."
Paul would go on in chapter 12 to describe how the body of Christ works together for the good over all and the mutual dependence. In chapter 13 he would describe the agape love of God which we know from Galations is the fruit of the Spirit (Gal 5:22) and from John is the mark of a disciple (John 15:8)
James calls this the royal law:
James 2:8 "If you really keep the royal law found in Scripture, "Love your neighbor as yourself," you are doing right."
Sin is not already present. Sin is born inside the individual heart.
Light has distinct properties and is known to be composed of seven colors. Darkness is simply that absence of light, sin is the void brought on by the absence of the righteousness of God. Our sin is not imputed to us until we are confronted by the law at which time it is exposed. It is exposed by the revelation of the righteousness that is revealed in Christ, unto all and upon all that believe.
Children are under the curse of sin whether they commit offenses or not, even being innocent they fall short of the glory of God. However you could make the case that their guilt is not imputed to them since they are innocent and don't understand either from conscience or the Law the righteousness of God. That in no way is the righteousness of God in Christ and if all sin and sin begins in the human heart then sin is already present or some might not choose to sin which is impossible. What you are talking about has been rejected by Catholic and Evangelical scholars as Pelagianism, a belief that Adam injured only himself. Were it not true that we inherited Adam's sin whether physically or spiritually then we could decided to be righteous by our own free will. If this is true, then Christ died for nothing.
I wouldn't be so hasty to jump to conclusions about Romans 5, you might want to take some time and think it through.
Grace and peace,
Mark