Breathing problem can be caused to be multiple reasons. You will have to show a doctor who can examine you clinically and then decide the cause of your breaathing problem.

There is no correlation between bilirubin and breathing problems. In very advanced chronic liver disease there may Respiratory issues with variable causes like hepatic hydrothorax, hepatopulmonary syndrome etc. But in your case, it's not looking like a CLD, You may have either Respiratory issues or anxiety which can cause such problems.

No bilirubin cannot cause this breathing problems. Please approach a gastro physician You can have some minor issue which might not be worrisome