K.
I just had my seven year old tested because she was so thirsty all the time and goes to the bathroom frequently. I was convinced she had it because my nephew found out he had it with the same symptoms(but really intense thirst/urination). They were able to tell me she didn't have it from a urinalysis(and I was very grateful to God!). I would think that if this was a concern at the hospital while your daughter was getting 'rehydrated', they would have thoroughly checked her out...Type I Diabetes is nothing they take lightly/put off for another visit. Talk to your pediatrician and have them test her if you can't stop the expected worry we moms are cursed with, but I would personally skip buying the monitor at this point.
Also, your daughter is unable to keep food/anything down because her stomach has built up a 'reflux' reaction while she has been sick. she felth better with the IV bag because it rehydrated her without having to pass into her stomach/through her very unsettled intestines(I'm an expert here because i threw up all throughout my 3 pregnancies and LOVED those IV bags...it was the only time I felt good!!!). When our house had the stomach flu at christmastime...after my son felt 100%, he ate a homemade plain hamgurger on a bun and still threw up a day later. His stomach wasn't ready for hard-to-digest foods and wouldn't be for a few days. If your daughter felt better from the IV bag, that means that she will no longer throw up from dehydration...but food can still cause it. If she is actually hungry, get her on the good old BRAT diet (bananas, rice-plain, applesauce,toast...and anything that falls in that category of exceptinally bland, plain food).We got through the flu by taking soda crackers,iced pedialyte and ice chips in very limited amounts to ease our stomach back into it. In fact, food is not even necessary until she feels "hungry".
One last thing: I'm no expert whatsoever, but I don't think throwing up has anything to do with diabetes. Get a urine test to put your mind/heart at rest, but it sounds like she is fine as far as diabetes goes.