I have a cough after being in the hospital?

I was in and out of the hospital a week ago for 3 days. I never spent the night though. I went in with stomach pain, a fever and a high white blood cell count. They ran tests and did an ultrasound and they sent me home saying i was fine after I started feeling better. Now, a week later; I have a very bad cough and sneezing. It's probably just a cold but could the two be connected?