HI Thank for choosing HCM I can understand your problem, yes of course coughing exert the downward force that causes the disc compression, as such you had history of sciatica then this force will bring back the sciatic nerve compression, to avoid this you will have to lie down at the time coughing, or at least sit down in chair,but do not take coughing bout in sitting position, have curative treatment for pneumonia, you can even try symptomatic treatment for cough, like anti tissue cough syrup, or expectorant, Have good Day,