Contact a psychologist and tell them your son is exhibiting symptoms of Gender Dysphoria. Find out if it's a phase or if he really wants to become a woman. He's young and it is best to start young. Also the changes can always be reversed up to SRS. However that's YEARS away. Be glad your kid had the courage to be honest about his feelings.
Try to be understanding.
Listen to his words. Yes, go and check up medically, but if he seems set on being this way, the best thing to do is be supportive. It can only lead to him to be more open, therefore getting in touch with his true feelings and emotions.
I may be wrong though...just saying.
Quit letting him watch the Jerry Springer Show.
No seriously your plan of seeing a psychologist sounds reasonable. I hid my desires from even earlier on than 10 years old. More like about 6 when it stopped being cute that I liked girly things. But I grew up in a different era. I never wanted to be a woman just wanted to be accepted and able to be open about what I liked. Having some anonymity here I can be a little open. Do what you feel is right but just love your son always. He's young but you just never know what you or they may remember in 50 years from now.
No one usually gets upset though if their daughters want to wear cowboy boots and jeans. That's just how life is I guess. Females acting manly or boyish are much more accepted than boys or men acting feminine. As a society we seem to value masculine traits more so than feminine ones. No easy answers really. At least he sounds like he has parents who care. Namaste.
Jamie can also be a boy's name. If I were you, I'd try to find out exactly why he wants to wear a dress before letting him do so. Or let him do so in private, and maybe he'll grow out of it.