feels like its never going to stop we thought a small friendly dog such as a bichon which we did homework on was ideal but everyone is upset at the constant biting (breaking skin) Tracey, firstly you are not giving all the good advice in previous posts, time....... this doesn't work in two minutes, one week, two weeks..... it can take weeks for some pups to understand, not because they are stupid but because their own instincts to play fight and act like a pup gaging their own strengths are stronger than anything else, he's enjoying himself and learning. (I know you're not, but he is)
Keep going with the puppy classes (KC reward based classes will be best for him, they will help you to teach commands) and continue with as already said the yelping and ignore plus time outs, please get that whistle, if he is ignoring you, it will help to peak his attention and help you train him commands quicker, again it may take weeks for some pups to learn.
When people have never had a pup like this it is hard to understand, we all expect some biting, chewing, scratching and tugging and yes it does hurt, pups play darn rough and some owners cannot even handle the basic puppy play......... but there are
some pups whom go above and beyond what we even expect and the training and your patience takes much longer, that is the only difference, you have a Bichon, try a GSD pup with the same attitude,

my brothers eldest was extremely hyper and took much longer to understand the world of domestic dog, he could easily have you bleeding and ripped into you, if you were not on the ball, never met a pup so rough, his other GSD was a dream to train, I once had the same problem with a Springer pup too, many before just the usual, that one, if I hadn't been used to training pups I'd have probably thought him a devil dog too. ;-)
Believe me, both of those dogs grew up to be very obedient, calm and loving dogs, you'd never believe looking at the adults what they had been like as pups. :-)
I fully understand why some owners become fearful and upset, you just need to persevere if you have a pup like this and I always find
that whistle invaluable the sound peaks attention and helps you to teach commands far quicker, verbal commands alone can have an adverse reaction, if a human's voice is too harsh, a pup will avoid the owner or continue to attack thinking he is being egged on by an angry tone, or if their owner has no air of authority a pup will ignore their owner and just carry on...... a whistle says neither and is generally listened to, you also need to avert this kind of play with some mental games.
No dog IMO is untrainable and the last thing you should do is expect too much, they are not all on the same level at the same age, everything at its own pace as previously said. Just ignore bad behaviour whilst keeping calm, and don't allow him to bite you or your sons, you shouldn't allow it, remove him and if he needs longer than a few minutes do so, stretch it to 30 mins, if this pup is not learning at all......just do nothing to entice this behaviour or inadvertently reward it.
Calm body language, calm tone, not overly looking at him with sadness in your eyes or hidden (you think) stress. Get on with other things and completely avoid eye and verbal contact with him. View him only as a pup who will take longer to learn to live with humans and get yourselves a 'well, so what attitude,' just walk away and wait until he is ready to learn, when he is 'good', in our eyes, (in his he is just being normal) you need to make sure he understands that too and reward him with a happy tone. :-)