Hopefully you would see more than just a gp, but an actual dermatologist.
Washing your face every day is a good idea, even within the shower, no harsh soaps. Not sure where the idea of letting oil build up would come from.
What might have been the advice is that the type of acne you have is actually further irritated by rubbing, since breaking the pores may result in further clogging elsewhere.
Tere are injections for some conditions of acne if ther are cysts that are developing because of this condition.
Allergic reactions might be occuring, but doubtful. See a specialist.