(Although the impression we get from Matthew is that Jesus would be much older that 13 days when they come. Herod kills the babies under 2 years of age based on when the star appeared and giving enough time for travel from the east and for Herod to conclude they weren't coming back to him. That sounds more like Jesus being at least a year old to me.)
January 6, along with December 25, was an early date of celebrating Jesus birth. This piece suggests that the way some early Christians (before Constantine, mind you) tried to calculate Jesus' birth date was based on:
- When he might have died, with April 6 and March 25 being two dates we early find attested
- The sense that Jesus was conceived on the same day that he died, giving a birth date nine months later of January 6 and December 25 respectively
We don't know what date Jesus was born, but meaning is not just a matter of origin. A tradition is only as meaningful to us as, well, it is to us. Christians have taken today as a day to think about the wise men for long over a thousand years. It's actually a bank holiday here in Germany.
There's nothing wrong with reading Matthew 2 today!