The image we have of Jesus is like it is (long hair, beard, long clothes, sandals) because that's what pilgrims looked like in the middle ages.
When the catholic religion was final;ly accepted and even made the official religion in many places, many churches were built and to help the mostly illiterate people of that time see what the priest was talking about they added statues and paintings of Christ.
They didn't know what he looekd like, since a lot of people thought he was just an imposter (I once read that at the time of Christ there must have been about 100 self proclaimed messiases/prophets) who would have bothered to actually paint him or even sketch him? And if that were the case, it would be one or two sketches, and the chance they would have ended up in Europe is alltogether slim. Especially since one of the ten commandments states that you are not to make an image of God, and as Christ supposedly was God in Human Form, early christians wouldn't have dared make an image of him, as it would have been a sin.
So the artists in medieval times didn't know how to depict Christ, they just used an image that people would know and feel familiar with. So a Pilgrim.
I once heard that the image of Jesus has changed somewhat through the middle ages, it just looked like what people looked like at whatever time the artwork was being made.
At some point they stopped doing that and all adopted the same image.
Threehundred years from now people won't know where the image of Santa came from, whereas we (some of us) do know. I think it's something similar
At least that's what I think
As for the relic, I have nothing to base my statements on, but I doubt it's the real thing. Just because I don't see how they would have kept it and how it would have passed on from one person to the other until it was declared the shroud of turin.