K.L.
I agree with one mom's suggestion that you may want to wake her up earlier from her nap than usual. Another mom's suggestion that she may need a schedule readjustment may also be what's going on. Play around with the nap, do it earlier and later to see if either helps, then try to wake her earlier a little at a time to see if this helps. With schedules, as you probably know having 2 others, it takes keeping one small change around for about a week to let it sink in and hopefully work. So all these ideas can take quite a while.
Another suggestion: she may have reflux, that's aggrevated at naptime. If she's just eaten lunch and lays down that may bring it on, causing pain. Then after crying that may be another reason she vomits as well. The pediatrician may prescribe her meds to help with this if that is the case. If it goes untreated it may be dangerous in the longterm so talk to him/her about it!
Just a note: my son has always been like that after his afternoon nap. Not as bad as gagging and vomiting, but being extremely touchy, cranky and prone to tantrums, sometimes all afternoon and into the evening. We've learned that he is just a sensitive guy after waking and we just take his cue in order to keep the peace, whether it's stick around him to play or leave out some toys and slowly back away...
Good luck!