Liver Cirrhosis - I am new. Anyone have trouble with their throat hurting in the morning and having?

Get this checked out by you Doctor, something else could be going on.

I've never heard of sinus drainage being caused by cirrhosis or in your case by diuretics prescribed to get rid of the ascites (fluid retention in your abdomen). Diuretics act on the kidneys and kidney function directly; the runny nose is definitely unrelated. The coughing could be caused by mild pulmonary edema (fluid in lungs) while the sore throat could be inflamed varices in your esophagus.
That you swelled up like you were pregnant indicates quite bad ascites You can't drink anymore at all if you want to extend your life. Healthy eating will pay off too. No Maccas, KFC or any of that greasy stuff. Fat is an inflammatory agent to your liver.