If you google "brown rice white rice" as I just did you will find loads of helpful information. Here is an example that addresses your specific problem:
http://chetday.com/whiterice.htm
I find the same 'stimulatory' effect that you do, but persevere because I love brown rice so much. It's worth the discomfort (unless really bad) in the knowledge that it's all good fibre !
As a matter of interest, what do you typically eat with brown rice, and what with white ? I will usually have white/basmati rice with curries, brown with Spanish Chicken, cold meats, etc. I don't help my own situation by adding hot chilli sauce to everything. Happy eating !