Hello
Persistent cough since 2 months ( dry ) but cracking sound present . You took amoxy &
erythromycin . As these both antibiotics are very useful in respiratory infection but you didn't got relief , this is a cause of concern.
The cough ( such type ) may be due to these reasons, these include:
1 Asthmatic allergic
bronchitis because you are a smoker ,hence such type of cough may be due to
allergy and this causes
bronchoconstriction , hence there develop cough and this type of cough usually didn't respond to antibiotics .
Diagnosis can be confirmed by physical as well as clinical examination by a physician.
2
Tuberculosis , this is also most common cause . As you mentioned that there is a shadow in X Ray chest and elevated E S R .
So these two tests are an indication of tuberculosis . Get in sputum (if not present nasogastric tube will help ) .If necessary get in protein purified derivatives(PPD)-Tuberculin Skin Test.
If necessary get in
bronchoscopy for confirmation .
3 Cancer as you mentioned that there is a density in lung so we can't rule out cancer . Get in M R I for confirmation.
However there are so many other reasons of such cough but deal as mentioned above .
In my opinion
consult a PULMONOLOGIST and get his opinion.