Hi Maximus, welcome to English Bulldog News.
Yes, your bulldog could have allergies. What food is he currently on? You should switch him to at least 4 star dog food, that is grain and corn free. I really like Avoderm, and I will let other owners pitch in with their favorites for allergies here as well.
This could definately be the cause of the "pink", as well as the pimples. Also make sure you are feeding out of ceramic or stainless steel bowl- no plastic. He could be allergic to the plastic. Wash to bowl after each feeding to remove bacteria.
After he is done eating and drinking, wipe his face, just as you would for a baby who ate spaghetti. If he is rubbing his face after he eats, this can cause even more allergic reactions and lead to your second problem, the entropion- I will now reply to that thread. Once you have the problem under control with a good food, you may no longer have to do the wiping down of the face.
Although you should wipe your bullies face daily, to make sure the wrinkles are clean.
We would love to see some pictures of your boy How old is he?