I did not have the issue in conjunction with a flu shot - but I have had an infant with a stomach virus. It's awful, I'm so sorry you are going through this.
My ped advised to try to keep getting fluids down. First, I tried nursing just for a few minutes every 30min to an hour. If the baby can keep it down for even 10 minutes, she'll keep some of the fluids. He also advised me that if that didn't work, go to pedialyte. Again, very small amounts in a bottle very frequently (it was like 1 oz every 15-30 min, or someting like that), so it's less likely to come up. If the fever is high and the previous dose of tylenol has worn off, your ped may also recommend a suppository dose of tylenol (FeverAll), available in any drug store, Target, etc. But you should definitely talk to your ped first for the dose.
If she really can't hold fluids down and is getting listless or is crying with no tears, then you need to go to the ER ASAP for IV fluids. Dehydration can be very serious in a baby because they don't have reserves.