A.A.
Go to Whole Foods and get their probiotic for infants (It's called Jarro).
Sounds like your son does have a virus. I would watch him very closely. Dehydration is a big issue with a lot of diarrhea/vomiting. If his skin color becomes more pale...or his eyes get that sunken look...or even if he starts acting lethargic, take him to the ER for fluids immediately.
You can help his fluid intake by nursing more frequently...or if you bottle feed, allowing him to take the bottle whenever he wants. The BRAT diet is designed to help diarrhea (bananas, rice, apples, toast). Give him the probiotic in his bottle (mixed with his formula or EBM) or you can mix it into a jar of food/yogurt, etc.
Definitely use your mommy instincts here. You may not have to "worry" for 10 days, but you may have to do something before then.
Hope your son is feeling better soon and this passes quickly!!