Full and bloated all the time + lack of hunger could signal a number of things. As boron says, H. Pylori may be a culprit here. However, you should also look into the possibility of delayed gastric emptying (gastroparesis) or issues with your gallbladder, (gallbladder dyskinesia) which could cause both.
Go to the doctor, ask for an H. Pylori test, then see about getting either an EGD (upper endoscopy), a gastric emptying exam, or both. Of course, the doctor will probably want to give you medications first, whichis good, but you'll want to ask for the exams, just to be safe.
These, by the way, are not the only possibilities. There are others. However, my advice is limited to my experience.
I feel full all the time and feel like the inside of my stomach is touching my chest. All I can eat is like three spoons of rice or something.