sounds like he needs pallet surgery, how old is he? you need to find a Bulldog vet --because if he is doing the phlegm he is having a bit of a hard time breathing or holding his head up high to sleep, and sounding kind of panting half the time. --and if the vet didn't check his throat out(look way back in the throat) he is not qualified to be a bulldog vet --they need to be way more observant . ask our forum about a vet in your area, or get a hold of the local bulldog breeders club(there will be one or more in your area) ask them who they recommend. we have a list on this site for many city's.
this surgery now days with a lazier will be around 700 to 900 lots cheaper than in the olden days , at 1500 a pop.
in the mean time, give him a big round pillow to set his chin on. (I use the foam tubes that kids use in the pool) cut to what ever length fits the space you have, he will love it . if he chews, put it in a pillow case. and put about a 1/8 of a cup of lemon juice in his water.---BUT -- this little thing grose ess your wife out --You might want to rethink keeping this Bulldog . FARTING -(only with Fromm --will this be kept at a minimum)BULLDOGS FART ALL THEIR LIFE !! slobbering---drooling while watching you eat. wanting their but scratched,and backing up to you to get you to do this. WE bulldog folks think this is endearing--not so much for other people!!!--- I'm sure you are going to get A slew of things from other people with other things they do .
get a good vet , and he'll need surgery after he is 10 months old (earlier -it will grow back)good luck, Linda