Yes you absolutely should go to the doctor and it's okay if he/she sees the cut and burn marks. In the self injury forum there are sticky posts that have very helpful ways to control those urges to hurt yourself. Right at the top of the forum are the 'sticky' posts. Did you know that when a person self injures they actually get a SURGE of endorphins and that's why if gives them some relief. You can also get the same feeling from some rigorous exercise - next time you feel like huting yourself, do 100 jumping jacks instead. You can also try writing on your arm with red non- permanent marker instead of really hurting yourself. Start exercising - it will give you that natural endorphin boost.
Don't talk yourself out of going because many people here are hoping that you'll get help. Believe me doctors have seen worse and heard everything - there's not much that surprises them. As the NIKE ad says - JUST DO IT. Good luck.