Woodhill, head covering is mentioned in the Bible though, in 1 Corinthians 11:3.
The issue is that Paul is not interested in Jesus' life or message at all. He focuses only on Jesus' alleged death and resurrection and what he sees as its significance. Why then, did Jesus (peace be upon him) spend three years travelling around with his disciples and teaching people if all of that is to be overlooked by Paul?
The first two books of Galatians clearly show that Paul opposed the disciples. There are many instances throughout Paul's letters which show him coming into conflict with groups of early Christians. The Christian groups who were close to Judaism, and their texts, were fiercely suppressed by those who would later be seen as proto-Orthodox (including the Church Fathers).
Yet, Dr. Bart Ehrman who is a renowned Biblical scholar with knowledge of Aramaic and New Testament Greek, argued that these groups were more likely to be closer to the original teachings of Jesus. He also argued, through analysis of all the New Testament books, that Jesus believed himself to be a prophet, and that later Christians developed the idea of him being divine due to prevailing beliefs at the time.
We Muslims also believe that Jesus was a prophet and that later distortions led to him being believed to be divine.
That's why I don't trust Paul's account of his spiritual encounter. Why would there be any need for a spiritual encounter when Jesus had already conveyed the message to his disciples and others when he was on earth?
Remember that Paul was often preaching to the Gentiles, who at that time were very hostile to the Jews due to their hatred of Jewish practices such as circumcision and not eating pork. Also, many scholars believe that the author of the book of Acts was a travelling companion of Paul and thus biased in his favour.