Yep, no point going to the ER. It wasn't from the shot, and it sounds like you have a normal stomach bug. If you get a high fever (101*+) then call your doctor. Otherwise, just rest and suc k on some ice chips if you can.
Tdap doesn't contain live virus so you aren't sick from it. Probably just a flu that's going around drink lots and try and rest
Sounds like you have a bad cold or the flu. If so, there's not much anyone can do, unless you get dehydrated and need fluids via an IV. Try to at least stay hydrated, even if you can't eat.
Call your doctor again tomorrow if you're still throwing up and having diarrhea - then they may one to do something to prevent dehydration. But it sounds like the best thing you can do today is rest and try to sleep. No need to go to the ER today.