I've been there and know all too well what you're going through. My almost 2 yr olds sometimes would pull away from me while I held their hand while leaving a store and would routinely pull their wrist or elbow out of socket. (nurse maids elbow) Simple remedy by the doctor manipulating it back into place. But just watch out for that 'going limp' thing when their having the tantrum if you're holding their hand or arm. You may end up in ER.
If your 16 mo. old understands that time-out means to sit quiet for a few min's, then it doesn't hurt. Pediatrician's recommend a minute for each year of age. You can put him where you can monitor him, and follow up placing him there with a firm, 'no!" He will eventually get the concept. If mine would scream and carry on in timeout and they had enough words to understand me, I would tell them, "if you can settle down and behave then you may get down." It's hard if they are still immature with vocabulary.....but they all seem to understand the seperation from what they were doing; fighting, screaming, hitting etc......with the drastic atmosphere change of "silent time out." They begin to associate the isolation with what they just did.
My two little ones who were back to back babies both went through terrible phases together......where they would let out an ear piercing scream in unison with one another. I would simply take them into a quiet room and sit with them if I felt what they were after was my attention. If one of them wouldn't stop screaming, then I would cross their arms in front of their chest and cuddle them very closely and firmly to my chest and rock them on my lap. (because they wanted to hit when they were in their tantrum) I would tell them "shhh...if you settle down I'll let you go play." That always worked.
I also try to think about their day and associate their behavior with what has happened or not happened that would put them in such a fit. Have they eaten recently, diaper need to be changed, are they missing a nap and did they miss sleep the night before? Or major issues could set them off, like crisis in the family or lots of visitors in the house will always turn my little ones around. One time, my little boy would not stop crying in his car seat all the way to the hospital for a checkup.....he loved his seat. After taking him out of the seat and checking him all over I was convinced he was just in a bad mood until I looked down and saw he had his little pinky toe bent over inside of his sandal.

Poor baby......so check all the fingers and toes and other body parts for injuries.
It can be frustrating, but as Megan said, be consistent each time they behave this way...what ever form of correction you use. But try not to correct while frustrated or stressed. Put him in time out first so that you can have a time out as well. Before going into get him, think about what you'd like to say to him to help the situation and leave him with a understanding of love from you, but that you won't allow him to behave that way. It does parents just as much good to have one.
I've even been known to put myself in a time out.
I'm convinced that about every 6 mo's little ones go through a major behavior change. It's like clock work!!
Good luck!!
myangelsinheaven