Aw shame, sorry to hear you're having problems with her skin. Very common unfortunately but I think your vet sounds a little judgmental... she doesn't have to deal with her allergies just cos she's a bulldog
My Boeboe's got sensitive skin too... she got better after he spay cos hers was mainly hormone related, but she does get hives occasionally. Hives can be caused by so many things, most commonly is probably food allergy. They can be allergic to basically anything, grains or a specific meat etc, it can be very hard to figure out. There's a test the vet can do that would show exactly what she's allergic too but I think she might be a bit young for that test still? @2BullyMama.
What do you use as shampoo? Two times a week sounds like a lot unless it some type of medical shampoo.
You could try to add Coconut oil to her food, it has helped Boeboe with her skin. About 2 tbsp a day, but start out with less so she can get used to it. The Coconut Oil does take a while before seeing results though... but it's good for them in the meantime