In answer to your question, it is possible but unlikely. You have probably come into contact with three separate viruses.
Also, your physician was, in all likelihood, checking for a bacterial cause for your illness, such as food poisoning
. Your bloodwork could return as having normal values and still have bacterial or a viral cause. One blood sample sometimes is not enough to isolate a problem.
Another explanation for your illnesses, may be foodborn. Have you noticed if you ingested any particular food prior to your episodes of illness?
To decrease the spread of bacterial or viral causes, be sure to wash your hands for at least 20 seconds with soap and hot water. This has proven, in studies, to be the most effective way to prevent disease.