Congrats on your new bulldog baby! I am sure others with much more experience than myself will be able to help you even better, but my guess is a food allergy. From everything I've learned, bulldogs are prone to lots of food allergies. Most need a high quality, grain free food.
Like Riggins....I had him on a good top of the line food but he was still having issues on his face. We narrowed it down to the fact that he is allergic to chicken fat. We switched him to Fromm Beef Friatta. Much better. We then added Answers Fermented Fish Stock and that changed the game. His skin has been 100% clear as long as he continues to eat the fish. I also give him coconut oil. People comment all the time on his skin and coat...how soft and clear it is. BUT...I will say that he does shed like crazy! Lol. I haven't met a bulldog owner that has said their bullie doesn't shed much. I think it comes with the breed. Riggins sheds an insane amount at certain times a year. We have black hardwoods and a white dog. Not smart on my part! And I warn people about wearing black when they come over. Lol.
Anyway, I would definitely try to get her on a high quality, grain free food. The lady that runs the rescue I foster for says that you need to work from the inside out. It's all in the diet.
Good luck! I hope her sore spots get better very soon!
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