I'm 43. i've been coughing hard & thought i was getting better, but i coughe hard about 40 minutes ago & felt a very sharp pain in my lower back (left side). now whenever i cough the sharp pain comes back intensely, like a pulled muscle or a stab?

Your pain could be from a muscle strain vs an exacerbated herniated lumbar disc with limited radiculopathy. It is not a rare complication due to vigorous cough. You should take some cough suppressant such as Mucomyst DM or Robitussin DM, use a back brace for a couple days and take Ibuprofen OTC 200 mg x 2-3, q8 hrs as needed for 2-3 days if you have no hx of stomach or kidney disease.