Mine has never tantrummed so I don't know if my response to grabbing/hitting would be helpful but this is how I deal with my toddler (2.5 years)
(I will just say here that I don't think my son never tantrumming has anything to do with my parenting- I think don't children are tantrummers and some aren't and it's just one of those things. Mine tests me daily in plenty of other ways! And his tantrumming days might simply be yet to arrive!)
Today he grabbed my face when he was getting overexcited. I immediately pulled away, showed my (genuine) shock and pain. He stopped in his tracks. I said very firmly "no! We do not grab people. That hurts me!" Then I said "I think there might be something you could say now to help me feel better because I'm feeling very sad." He said "sorry mummy" and gave me a cuddle. As soon as he did that I said "thank you that's so nice, I feel better now. Remember we don't..." and he replied "grab people." Then I switched straight back to everything being light and fun again. All forgotten and move on.
I do this with anything like hitting or grabbing.
Also today (not quite tantrumming but acting really silly and getting hyper so might be a helpful tactic), he was getting restless and silly in a cafe and lolling about on his chair, waving his hands around while people are having hot drinks, started to get hyper and a bit loud. I warned him once, then twice, to sit nicely on his bottom because he might knock something off the table. The third time I removed him from the cafe and took him to a quiet spot away from people outside and had a stern word.
As before I get him to repeat back to me what I've said so it's understood. "When we go back to the café what are we going to do?" "Sit on our bottoms on the chair." Then again snap straight back to light and fun again. I think it's important they see that if they're listening to you, everything is pleasant and fun. If they're not listening, the fun stops. I always physically remove him from the situation to really highlight this.
16 months is still so young and tbh at that age I just wouldn't feed a tantrum. Let her rage it out, make sure she's safe, remove yourself if she's lashing out at you and keep what you say simple "no, we don't hit/kick/bite" then move away/move her off you. As soon as she stops tantrumming I'd go full on with attention and fun, straight back to playing with her.