nothin to worry about I had something similar this week, I was pretty sick for a few days (intense fever, fvckign had to change clothes twice at night cuz I was drenched) but the coughing remained for a few days afterwards without fever. Kept taking some antibiotics and it went away eventually.
The second night of sickness I couldnt sleep at all cuz my brain activity wouldn't shut down, weirdest and most uncomfortable thing I have ever went through. Experience something like that or is it just me?