Having had bariatric surgery and been on blood pressure medicine for years... I certainly know well about dry mouth and stuffy nose at night.
First, what causes these side effects when on Flomax is the diuretic part of Flomax. That essentially tells your body to take away moisture and send it to the bladder. One of the main areas that the body takes moisture away from is the mouth, nose, and throat.
To alleviate dry mouth... simply buy a few bottles of Vitamin Water and keep them bedside. Vitamin Water works well to remoisten the mouth and throat and helps prevent constipation (another result of the diuratic). It tastes great and is very effective on dry mouth.
DRY nasal passages lead to irritation of the nasal membranes. Go to the drugstore and buy a few small cans of "Simply Saline Nasal Moisturizer". Sroay before you go to sleep and you might need it once more as the night wears on. It is cooling and feels fine whether you snort it in or not. The body IS mainly composed of saline water anyway. It is the perfect moisturizer. It will not wake you up. This will eliminate the inflamation and thus eliminate the stuffy nose. AND... unlike nasal decongestants... there is no "rebound".