your low
WBC count could be the result of antibiotic and other medicines usage
it will get better in few weeks to months after stopping them.
you need to work to improve your immunity to overcome
cough it could be just allergic
bronchitis or viral bronchitis or fungal
first try to identify the triggers and avoid exposing yourself
dust
pollen
exposed to too many birds (Poop)
chemicals that you clean kitchen/ toilets
spray chemicals
tobacco
second build your immune system by eating healthy nutritious diet
I am a physician but inclined to use natural products available at home
so drink
raw honey lemon ginger juice syrup
milk with pepper turmeric powder
garlic pods crushed with pepper and salt cooked or raw
the above ingredients build immunity while detoxify and eliminates phlegm from respiratory tree.
last but not the least important is doing breathing exercises
this sounds tough job as u r alone but writing to help itself signifies u r motivated to get better so worth a try
good luck