I'd also recommend changing your diaper brand. Better diapers will neutralize the urine so it won't give you a rash, at least not with a single overnight wearing. It may itch a tiny bit, but you won't have a rash. Also, drink more water. This will dillute your urine so it's not so acidic.
Most people don't have this problem even if they sleep in it because all the big brands have a chemical in them that neutralizes urine to prevent odor and rash. In fact, some sites actually include urine neutralization speed in a diaper's rating.
However, if you buy generic store brands or other low-end brands, they may not have this chemical, or not enough of it to be effective. These diapers work acceptably if you change them immediately after use, but if you don't you will get a rash. If you are running into this problem, change your diaper brand.