How long has he been taking the Allegra? It may take a few days for it to work. Does the rash itch? If so use a steroid cream on it.
This is not an emergency. It is extremely unlikely that his throat will swell up. Do not take him to the ER. After reassuring you they will just tell you to take him to his doctor. They are not trained in allergies. They would probably advice you in the same way your doctor did. You won't know any more and have another bill.
I have multiple allergies as did my aunt and now my grandaughter. Usually when I get hives on my body my mouth and throat are not involved my mouth and throat get itchy when I eat food to which I'm allergic or have a sensitivity to. I don't also get hives.
Just know that if this an allergy or not it may take time for the doctor to figure it out.
I suggest you call his doctor and ask what the next step is. He may refer you to an allergist or he may try a different approach.
Another mom suggested benedryl. My granddaughter's doctor recommended that. Both my granddaughter and I use that for allergic reactions. The hives, itchy throat always go away with 1-2 doses.