Hello and Welcome to ‘Ask A Doctor’ service. I have reviewed your query and here is my advice.
Considering the symptoms, in my opinion you have been going through a bacterial infection which started as an upper respiratory infection
and progressed in acute bronchitis(probably from streptococus). This infection usually mimics a viral syndrome
and it's difficult to diagnose only by the history.
The rash may be related to strep infection but it also occurs in viral infections, they are both commonly followed by body rash.
You can consult your doctor for a physical examination of the rash and he will probably order a rapid antigen test or a throat culture
which uses a swab sample from your throat to detect potential streptococus.
It's important to make the right diagnosis, because if you have strep bacteria, you need antibiotics treatment.
Menawhile if you still have cough, you can use guaifenesin
to thin your mucus.
You can also use ibuprofen
400 mg if you have any headache.
Hope I have answered your query.
Let me know if I can assist you further