“Not only did Paul took four other followers of Messiah, they immersed in a mikveh (pool of water), and then offered animal sacrifices (the vow mentioned was the Nazarite vow from Numbers 12). They measured the time of the vow by the cutting of the hair, offering the hair on the alter, and then offering animal offerings.
None of that is stated in the text. Paul was trying not to offend the Christian Jews. However, go read the book of Romans and other books by Paul to hear how he regarded the efficacy of sacrifices. However, if you want to shave your head, go for it.
Clearly you mind is made up and you seem more interested in thinking you are right than investigating what the Bible might say to be true.