I think you need to define 'very aggressive'
If he normally seems to have a pleasant and reasonably relaxed nature, it sounds like he's just getting exasperated in a puppy way, but nevertheless those teeth can cause a lot of damage, but by putting him down (even though you said NO at the same time) he's achieved exactly what he wanted, so his 'aggression' worked.
Watching litters of dpups interacting they are very aggressive little things and make each other really scream sometimes, and will fight over food if allowed, snap at each other, these are all instinctively normal things for them.
If you are holding him for a reasonable amount of time for a dpup and you are clearly doing this for his own protection then you are doing nothing wrong.
what i would do is introduce today, a quick pick up, good fuss, a treat and then put back down, turn and walk away, the fuss is at time of being carried, not when put back down. If you do it quickly the first time just literally picking him up to say clever boy, fuss and back down, walk off. try that several times over a couple of hours and then hold for a very short while continuing the praise, noticing whether dpup is all tensed for action or legs dangling relaxed. Its all about the timing, and then progress to taking a couple of steps. because its a very quick exercise its only going to take such a little amount of time, but it takes the preparation.
I would repeat this many times today, and increase the time and always notice the state of relaxation. If dpup is relaxed when you first pick up then treat straight away, if dpup is immediately struggling to get down and starting growling and snapping then be prepared for it - put leather gloves on and tie your hair back and wrap in a towel if needs be! so that you can hold until he gives up, and the very moment he does give your reward and put back on floor.
I carry my dpups around a lot (because of steps and other dangers for them when so little) that i find it a bit weird that he is creating so badly. I am forever carrying sleeping dpups back to bed that have played and crashed around the place, and picking them up to take out so there's no 'accidents' indoors. I wonder how much they have been handled because being high up must be quite strange to a dpup not used to it perhaps.
Good luck and let us know how you get on?