I have twins and personal experience in this. One of my twins would also bang his head against things. He is five and still hits himself in the head when frustrated or tired. Try a different doctor ASAP. Personal issues about race can sometimes cloud professional opinion. But to be fair, your son may not be old enough for evaluation too.
Self-violence can be a sign of something else worse. If he is only hitting himself in the head area, it can make neurological problems worse. The brain is a sensitive area. Try getting more information about sensory disorders. Read this article. www.autism.org/sibpaper.html. It's written for clinicians but I love the wealth of information on this website.
A child who can't talk well often has problems explaining he doesn't like a certain color, lights, texture, etc. It is also harder for children to control behavior when tired and/or overstimulated. Keep a diary of when he bangs his head, you might find he can't stand the color RED. Then you can avoid shopping at Target. That type of thing may make it bearable regardless of doctor's opinion. It'll make for a happier child regardless.
That twin was later diagnosed with autism for this and other behavior that was hard to ignore later. Don't give up on your kids and don't let them be ignored. Twins are different that singletons. Find a twins group to discuss your problems and yes there are many, many online only groups to fit your schedule. (100+ on Yahoo Groups!) There are also groups online for parents raising multiracial kids. Contact me if you need website addresses.
I also agree with the mom who mentioned ECI later. Services are free or sliding scale if your child has developmental issues. They also do home visits so you don't have to give up work either.
Good luck