That’s a very clear sign the edge is not good enough.that slightly painful tugging
Besides,
I would not expect a good and smooth shave from a barber. They are not fanatics in getting their edges sharp and comfortable. Their job is to shave, not to spend time honing on expensive stones. If their edges are half decent (or maybe even below), that will do it for them.I had a professional barber shave me with a straight and even that wasn't particularly comfortable. It just felt tuggy