Hi, We are not doctors on these forums but I am a microbiologist and can give you some advice. Firstly did the doctor do a xray of the lungs and listen to your lungs? They should do this to make sure you have no pneumonia? Do you have a fever? If so how high? If they haven't done these things they should have. You might need antibiotics. If those things are clear you might have bronchitis which will clear on its own over time. Usually, bronchitis doesn't make eating worse but exercise might make you cough more. You can still walk but not a fast walk. It depends on what they did. The other blood tests sound like you have anemia. That has nothing to do with your cough usually. You can get some other tests to check for anemia like a blood iron test, ferritin, vitamin B12, folate. Have you seen any bleeding like dark stools when you go to the toilet? does it hurt to press on your stomach or side such as the upper right or left side or lower right side etc? Do you have night sweats? Hae you been tested for current TB? Do you have a lot of fatigue?
Just trying to figure it out. Did you have a cold or flu before this happened?