As Erica said, its a good idea to develop a relationship with your hemotologist so you have a plan in place should you need treatment. Having discussed your options so that you can go home, research and assimilate the impacts, makes it a lot less stressful when the time comes that you have to treat.
Illness impacts all of us differently. For most, the counts will drop during an illness and for some they will raise. For me, it depends if it's baterial or viral, I can go either way. Definitely antibiotics trigger a drop for me. Once you shake the flu, you may bounce back. Or you may need a treatment to bring you up.
I can have nose bleeds at high counts. Mine are triggered by seasonal changes and low humidity and/or allergy stuffiness/dryness. Your's may be related to the flu or they could be symptomatic of the lower counts. See your doctor about coughing up blood just to be sure. It's as likely that it may be that your having a minor nose bleed that's draining into the sinuses and when they drain that's what your experiencing when you coughing up blood. Your sinuses don't drain when your laying prone, which is why you tend to cough a lot when you first get up and they start to break loose. I'll often see blood in the sputum if its been really dry so that I have minor nose bleeds.
"I am an old man and have known a great many troubles, but most of them have never happened.\" — Mark Twain\\\\\\"Worry is a misuse of the imagination.\" — Dan Zadra