Sounds like a stomach virus, when you can get it down drink a bit of peppermint tea to help with the nausea and make sure to keep taking in fluids, otherwise see a doctor for antibiotics if it doesn't go away soon, as persistent stomach viruses can be extremely uncomfortable and sometimes take too long to beat with your own immune system that it leaves you feeling stuffty for days.
Dizziness may stem from dehydration (which if you have been puking w/ dirrahea, its more likely you are experiencing) so keep drinking water.