Yes food allergies can be the reason for reflux.
In this case though they usually aren't true allergies, but intolerances. That is to say that the LO's often 'grow out' of their reactions to the foods. The 'reactions' that cause the reflux-like symptoms are usually inflammations somewhere in the gut to the proteins in the foods. Some LO's get inflammation in their bowels and it shows up as bleeding in their poop. Others (like my DS2) get it in their esophagus and it shows up like reflux.
My DS2 had a milk protein intolerance (= MPI) I ended up cutting milk out of my diet for 8 months. Initially I didn't notice any difference. I went to reintroduce milk back into my diet after 2 weeks, and the screaming, back arching, poor sleeping all got SO much worse. So we stopped it again and things went back to slightly crappy instead of completely crappy.

(Keep in mind he has reflux as well, so that complicates things.)
It can take 2-4 days for the proteins of milk to get out of your system and breastmilk. It can take up to 3 weeks for any damage in the esophagus or bowels to heal in LO. I'm not sure how agressively you are looking at removing milk from your diet, but to go truly milk free you need to be a big label reader as it goes by many hidden names in foods. I know there is a link (on the FAQ of this board - I think

) to a page with a bunch of different names.
You may also want to avoid any other mammal milk (ie goats, sheep) and soy milk for a good month or so as the protein chains in them are similar to the dairy protein chains.
HTH