Primal diet is cavemans diet but I like to call it more like a lifestyle as doesn't diet mean eating a exact kind of food for a period of time ?
I eat lots of meat and fat (fish too), occasionally including some fruit. Eating only meat and fat is perfectly fine as long as you have balanced omega 3 to 6 and meat is not cooked too much.
Actually primal diet means eating lots of raw meat but it's not necessary to eat it raw as long as you won't be eating like this for years. I eat beef all raw but cook some pork what is actually unnecessary but I have digesting issues with raw pork (Maybe not enough right enzymes yet ? )
Take a period where you eat only meat and fruit. When your allergies have cleared up ( If not then it's not caused by the food you eat. It could be immune reaction to whatever there is around you and that is where prasites as I posted before come to help) start eating vegetables one by one (If you still want them.. :)).