Razer burn? If you shave both those areas..
If that's the case, just make sure you use enough shaving cream/lotion and moisturize afterwards.
The only other thing I can guess for the underarm problem would be a possible deodorand or anti-persperant allergy. Most are sold mixed together. Try finding a deodorand without anti-persperant, then try an anti-persperant without deodorant. If one stops the itching, use that from now on.
As for the private itching, is it inside your body, or outside?
Hm... You may want to do a little research on Yeast infections. They're not that bad and not difficult to treat. But be sure you really do have it before you begin any treatment