How can you cure cold sores and mouth ulcers? Is there a rinse?

No cure- it's herpes. More than likely it's caused by a herpes outbreak (hsv-1 typically). Drinking acidic fluids can make the situation worse; with poor dental hygiene, the burden of bacteria will allow the ulcers to fester. In certain instances, medications such as acyclivro can help. Otherwise, the burden of oral bacterial can be tamed by the use of either listerine or a warm salt water gargle for 1min, 3 times daily.
Cause unknown. Mouth ulcers, e.g. Canker sore, apthous ulcers, ..Take 7-14 days to heal. If you don't have high BP issues, warm salt water rinse helps alleviate pain. Systemic condition can affect the duration of healing. Laser treatment can reduce it to 3 days. Check your diet and make it sure you drink plenty of fluids to hydrate your mouth. When a trauma occurs in an area, prostaglandin is released.