There's a blood test which will determine the allergens, but that thing costs quite a fortune. 
Ah, I think it could be the exact thing you're talking about, as mine tends to furiously bite/ lick on those things, popping them and by the time we noticed, they're like blackish/ bloody red spots.

I recalled the vet also told us to avoid feeding him chickens/ eggs since they are one of the culprits. Will try to restrict him access to it and hopefully things improve.

Funnily the secret feeding thing happens to mine as well
Yeah, pimple it seems.