I have some questions for you.
Does your horse's tack fit for sure? Any other pain related issues that could include back pain?
There are several things that could come out at a trot but not at a walk.
Have you lunged or round penned the horse without tack, with tack, with and without another rider on top and not using leg cues? Tack can fit differently with the added pressure of a rider.
Do you do any groundwork? If so, is he respectful? Never mind, I just reread your post and you have said that he has attempted to bite you.
In that case, he needs a good deal more groundwork. Making him move his feet where you want is the best. Backing him up is humbling to a horse.
There are several ways to accomplish groundwork, you just need to find a method that you like.
The bad news is that you are worried about it becoming a habit, I would say it already is, the good news, it can be trained out of him with groundwork. (As you can guess, I believe in groundwork, lol.)
Three is very young, that is for sure, but, the longer it goes on the more the horse will think he's in charge and the leader.
I have seen people really get on a horse for pinning their ears, kicking at you while under saddle. You could ride it out if you want/can, but, I still prefer to handle it with ground work that transfers to the saddle. If you can fix it on the ground, your problems will be easier or even non existent under saddle.
There are many training dvd's out there to choose from.