J.,
Having two children can be really hard when they are both relatively close in age. But, to be able to keep both children from hurting themselves as they get older you need to establish firm rules and consequences now.
16 months is more than old enough to understand the word "no" and your little guy is learning what reactions he can make you do when he pushes the "no" line a little bit more. It has turned into a game for him. If you don't start to put firm boundaries on his behavior now, then as he gets older he will continue to push the "no" boundary and may put himself into a very dangerous situation because he is playing the game.
Your baby also needs to learn how to be without you even for a few minutes. Try playing hide and seek with the two children to teach your little one that he's not in danger just because he can't see you. Slowly stretch out the time that you stay hidden in a fun way so he learns how to be by himself and with just his sibling without panicking.
You didn't mention when your baby wakes up in the morning, but if it is early, then you might want to consider transitioning him to an earlier bed time so he can get the sleep he needs. He should be sleeping 12 hours a day right now between sleeping at night and afternoon naps. If he sleeps until 10 in the morning, then he is probably getting the sleep he needs, but you may want to try to transition him to an earlier bed time so he is awake earlier in the day. This will make it easier for you to get the rest you need as well.
If he is an early riser, then I would recommend you put your little guy down for a nap in the afternoon after lunch. If he cries for more than 20 minutes without stopping, then go in and try to comfort him, but don't take him out of his crib or pick him up. Rub his back and talk to him softly (even if he is screaming), then once he calms down leave the room again for another 10 - 15 minutes. If he is still crying go in again and touch him, speak softly again until he calms down. Over a few days he will learn the new routine and learn how to self-sooth himself, but it will be a rough few days.
If he starts a tantrum and throws his toys around the room, then remove all the toys from his crib for the rest of the nap. If he starts to hurt himself, hug him in your lap with his arms and legs pinned to his side (firmly but not painfully). Calmly tell him you can't let him hurt himself and he won't be let go until he stops the behavior. I had to do this with my son only once right around this age. He learned very quickly that he did not like that type of controlling hug and never tried to hurt himself again. The key is to remain calm no matter what he does or tries to do. You are his role model and he needs to see you staying calm no matter what.
Eventually your little one will learn how to behave politely while your attention is elsewhere. Babies / toddlers need consistent consequences so they know what will happen if they misbehave. It takes a lot of patience and will power, but I know you can do it. I hope you have a Merry Christmas.
C. J.