Can you get a low blood platelet count if you are sick from just a cold or stomach virus?

Usually gets higher: Platelets are among several "acute phase reactants" which increase with illness. They can go down with infections, but this can be a bad sign of some other disease which lowers your platelets, like felty syndrome (and many others).

Yes.: Viruses can cause suppression of the bone marrow causing any combination of anemia, low platelets, and low white blood cells. After you recover from the virus, your bone marrow will recover and so will your counts. If they don't, other causes will need to be considered. In addition, some people develop immune thrombocytopenic purpura after an illness (an autuimmune destruction of platelets).