No, we don't know what Jesus looked like; photography hadn't been invented then, and no one in Jesus' day painted His portrait. Over the centuries, artists have tried to show what He might have looked like but, at best, their efforts are only the products of their imagination.
Has the actual burial cloth of Jesus been preserved (with the apparent image of a crucified man impressed on it), as some believe? Perhaps, although no one can say for sure, and I doubt if anyone will ever be able to prove it with finality. The Bible doesn't mention what happened to the cloth, nor does it recount what happened to any other object associated with Jesus (such as the cross on which He died).
Why is this? The reason is because our faith is to be in Christ -- and Christ alone. Our faith isn't to be in things; our faith is to be in Christ, who alone saves us by His death on the cross and His resurrection from the dead for us. The Bible says, "Through him you believe in God, who raised him from the dead and glorified him, and so your faith and hope are in God" (1 Peter 1:21).
Never forget: Jesus Christ is alive, and even now He sits at the right hand of the Father in heaven. And because He does, "He is able to save completely those who come to God through him, because he always lives to intercede for them" (Hebrews 7:25). Make sure of your salvation, by putting your faith and trust in Christ today.