Yes, using tap water with a sinus rinse could potentially be related to irritation and nose bleeding. It is recommended to boil the water for 5 minutes and let it cool before using it for nasal hygiene to prevent the risks associated with microorganisms in tap water. Additionally, if you tend to blow your nose forcefully, this could also be a contributing factor to nosebleeds. It may be helpful to try and blow your nose more gently and irrigate with less force.