Throwing up blood sounds pretty bad! You should go see a doctor as soon as you can if this continues to happen.
In the meantime (if it turns out you are generally healthy), I would suggest cleaning up your diet (no processed foods, junk foods, and generally problematic foods such as dairy or gluten). See if your symptoms improve based on your diet (give it a good four-five weeks of clean eating to see any effect).
ALSO I would definitely recommend going to a gastroenterologist for testing (colonoscopy, stool, blood tests, SIBO test, tests for parasites). Who knows what they might find?
I'm not really sure what you mean by 'leaking in the morning'- are you talking about an inability to hold in gas? That could potentially be caused by weak anal sphincter muscles. Try Kegel's exercises.
Keep in mind that going regularly to the bathroom (around once a day) is important, but it's also rather important not to strain too much (this could lead to hemorrhoids, prolapse etc.). Try to drink more water and exercise regularly. This change in lifestyle (upped water intake, regular exercise, clean diet), should most definitely give you some improvement in a matter of months if you stick to it (assuming that there is no clear medical issue that the doctors can find). If there is NO improvement whatsoever in a matter of six months, I would revisit the doctors for more tests as clearly whatever is wrong is too difficult to beat without any guidance/direction.