Puppy nipping and agression

Hi! We need advice. We have a 5 month old English Cocker puppy who is challenging and frustrating us. He is showing agressive behavior by nipping our toes, jumping up and nipping at our legs, and barking back when corrected. We have been told to ignore the behavior and he will learn that he is not being rewarded for his actions, but when we try to walk away he jumps on us and tries to nip the back of our legs. He has actually put holes in our jeans when his nipping makes connection with us. We have tried holding him down with a firm 'no' and tried to be the alpha person but once we let him us he just continues his behavior. We give him plenty of exercise through play, walks, trips to the park to run on a 30 ft. lead and that tires him out but then when he wakes up he starts over again. He has been to basic obedience classes that we continue to work on. Help!