Hi,
When was the last time you got your teeth cleaned? If not more than an year then u need to see a periodontist and get your teeth cleaned.
Gum bleeding can be because of gum inflammation which occurs due to tartar accumulation. And teeth sensitivity can be due to various reasons so you.need to see the doctor for that. If you have a night clenhing habit then also lower teeth can get sensitive.
Next Steps
meanwhile u can use a desensitising toothpaste such as vantej toothpaste by dr.reddy's or sensory rapid relief toothpaste.
Health Tips
use a soft toothbrush.