Yes! she will be OK! You just have to find out to what she's allergic. Hives are an allergic response, usually to something that contacts the skin.
I doubt that this is a milk allergy. It sounds more like she is allergic to something that contacts her skin. Even tho I have a lot of allergies the only time I remember getting hives was after going to a movie. The hives were on my back. I suspect something was on the fabric of the chair.
Do you give these medications with food? My granddaughter takes Zyrtec after breakfast.
Many years ago I vomited every morning. I learned that the cause was my multi-vits with calcium. Calcium is very irritating to the stomach for some people.
My granddaughter had a milk allergy when she was a baby. She never had hives. Actually I think her mother discovered the allergy during a visit to address several issues. She outgrew the milk allergy by the time she was 5.
Have you tried not giving her anything in the dairy family? If she's allergic the hives and vomiting will stop in a couple of days.
I have a lot of food allergies. They have never given me hives or caused me to vomit. When I was younger and ate a lot of the food I eventually learned that I was allergic to I'd have an upset stomach but never vomited. Now, I get an itching in my throat and ears. In my experience a food allergy first shows up with mild symptoms that increase over time.
It is possible that she has a stomach bug that's unrelated to the hives. As a teen I did have hives after a bee sting. I've not had any reaction to a sting since then which probably means the bee had something either in the venom or on his stinger to which I was allergic.
I'd try switching to a different detergent, using a mild one recommended for babies and those with sensitive skin. If you use a fabric softener I'd stop that. First, I would run a clean cycle on your washer using Chlorox or vinegar and clean the dryer drum with a vinegar solution. If your washer doesn't have a clean cycle just run it thru a regular cycle without anything in it except the vinegar or chlorox. If you have hard water add a water softener.
I would also try not using any soap or lotion on her for a few days. Rub cortizone cream on her hives. The cream should soothe them in an hour or so. Sometimes it works immediately.