I'm sorry, but your fiancee may be right about what he's allergic to. Allergy symptoms are the same, regardless of what the person is allergic to. Different people can react differently to the same allergen, but it is unlikely that the same person will react differently to different allergens, except in regards to intensity.
For example, I have always been somewhat sensitive to most animal dander, saliva and urine. I experience at least mild nasal and eye allergy symptoms to dogs, cows, horses and guinea pigs. But I used to always have severe reactions to cats. The type of symptoms weren't different; just how bad they were.
I hope this is making sense to you. The only way to know for sure what your fiancee is allergic to is to have allergy skin testing done. But that can be expensive and time-consuming, and requires that he see an allergy specialist. He can start the investigative process right away by keeping a symptom diary.
In this diary, he should note when he is having symptoms, what they are, how long they last and what he was doing or coming into contact with in the hour before symptoms began. Also, he should note if anything relieves the symptoms. After a week or two of this journaling, he may be able to notice patterns in his symptoms that can give clues about the true allergen.
If it does turn out to be the dog, then you'll need to make a decision what to do. If you decide to keep your dog, then it's important to keep him out of your bedroom altogether (and certainly OFF the bed), but perhaps also out of your main living areas, like the living room couch. Since you are also bringing home pet allergens, it would be a good idea for you to shower and shampoo as soon as you come in the house and before getting too close with your fiancee.
Good luck!
Kathi