My 3 yr old son has had diarrhea for 4 days and vomiting for 3. He has no fever but can't hold anything down except water. I don't know what else to do?

Check dehydration. Your big concern right now is dehydration as well as what is actually causing the diarrhea and vomiting. If he has decreased urine output (generally if he is peeing less than three times in 24 hours), if his mouth and eyes are dry (no tears when he cries) then he may need additional hydration. In general, viruses will last less than 48 hours and so i would also recommend seeing your doctor.
How does he look? If bad, he may need to go to er for IV fluids, or if not, his doc can also prescribe meds that can stop vomitting so he can rehydrate orally, **small frequent amounts**. Any kid above 2 will not drink pedialyte so next best thing is sports drinks then 7-up or sprite; brat diet (bananas/rice/apple/toast) bland foods stay down better. He can get better faster w. Orals but he may need some help.