I got a new domain and put a 301 redirect from my old one to my new one. The problem is that I don't see in google webmaster tools where I can update this. I'm kind of confused and at this point I don't know what's the best thing to do. Delete my sitemap and resubmit it with the new domain? How bad will that hurt me?
I wouldn't update anything. Just let the 301 redirect work and in webmaster tools add your new domain name.
In my opinion it is better to redirect old sitemap to the new sitemap in the same way how is redirected the whole web. The redirect will help to the bots to find new sitemap quickly.