As the owner of 2 allergy dogs myself, I can completely understand your frustration and wanting to figure out what is making your little bully so miserable.
Because he is a bulldog, who as a breed are prone to allergies, I think the absolute best thing you can do is to ask your vet to do a VARL test (you can read more here: http://www.varlallergy.com/ ). This is an allergy test that will tell you, without doubt, what he's allergic to, and then you can work to eliminate that from his world.
Unfortunately, my dogs both ended up being allergic to grass...luckily though we live in northern MN where we have snow on the ground 6 months out of the year.
Once you get the allergens identified, you can get him on a medication such as Temaril P or Atopica which will help his symptoms and make him more comfortable.
In the meantime, here are some 'home remedies' that I've found that really seem to help make my guys more comfortable:
*For some itches, we suggest soaking in a baking soda bath. Adding 1 cup of baking soda to a tub of warm water and then soaking 30-60 minutes. Take dog out and let them air dry (this works best if done outside or in an area where there isn't carpeting as wet dogs drip...a lot). Local itches can be covered with a paste of 3 parts baking soda to 1 part water.
*Oatmeal is an old favorite. Adding 1-2 cups of finely ground oatmeal to a warm bath sometimes can calm even the most irritating of itches. Just make sure the water isn't too hot, or you'll have breakfast for a week in your tub!
*Lots of folk remedies call for using lemon to help with itching. They contain anesthetic and anti-inflammatory properties that may help reduce itching. If nothing else, your dog will smell good!
*Splashing the affected skin with basil tea can help reduce itching as well. Basil contains large amounts of a substance called 'eugenol', which is a topical anesthetic. To make the tea, place 1/2 ounce of dried basil leaves in a 1 pint jar of boiling water. Keep it covered to prevent the escape of eugenol into the air. Allow to cool, then dip a clean cloth into the tea and apply to itchy skin as often as needed.
*Mint tea works about the same way, except the anti-itch property is menthol, not eugenol. To make the mint tea add 1 ounce dried mint leaves to 1 pint of boiling water. Cover and allow to cool. Strain the leaves out and then dip the clean cloth in the tea and apply to the itchy areas.
*If you're saving the basil for spaghetti sauce and the mint & lemons for a glass of lemonade, you can use thyme tea. Once again use 1/2 ounce dried thyme leaves and 1 pint of boiling water. Cover and cool. Strain and use clean cloth to apply to affected areas.
I hope this helps!!