No, we don't know exactly what Jesus looked like; the Bible doesn't tell us, nor did anyone paint His portrait while He was alive. Artists have tried to imagine what He might have looked like, but at best their efforts are only guesswork (and sometimes clearly wrong).
What is clear from the Bible, however, is that Jesus didn't come just to save one race or one ethnic group. He came into the world to demonstrate God's love for the whole world -- for people of every race and culture. By His death on the cross and His resurrection from the dead He opened heaven's door to all who will come to Him by faith. The best-known verse in the Bible makes this clear: "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life" (John 3:16).
Don't let the mistakes (or even the prejudices) of a few keep you from Jesus. Instead, thank God for His love for you -- and make that love a daily reality by opening your heart and life to Jesus Christ. Ask God also to give you a new love for others, no matter their race.
Thank God, too, that in heaven all the barriers that currently divide us will be erased forever. Then we will praise God together, thanking Him for sending His Son into the world to save "men for God from every tribe and language and people and nation" (Revelation 5:9).