Dog nipping too hard- am I responding correctly?

My pup is a 3-4yr old rescue, GS mix. We've had her for almost a year. Her behavior was pretty atrocious in the beginning, but it's very obvious she was abused, so I only focused on the most negative behaviors first.

Now overall she's manageable, and I know it takes a lot of time, and I don't mind. She's not aggressive, but she is extremely sassy. She will argue, or express her discontent by snapping at the air. I understand that is a very common behavior with GS, and it looks much worse than it is. To me she's just talking. She's very much a Velcro dog and affectionate.

Unfortunately though, sometimes during play, or if I'm just walking through the house and she wants attention, she runs alongside me and gets a hold of my pants or long sleeve. She does not do it to exposed skin, so I think she just doesn't know she's actually getting me. She really clamps down hard, and she almost broke the skin on my wrist. I yelped like a puppy and she immediately let go, and tried to lick my arm. I took it as an apology, but I need her to stop as I'm afraid she'll accidentally get one of the kids or scare someone.

Aside from ending play when she acts like that and yelping, I'm not sure what to do? I don't believe in physically punishing, especially knowing her past. But as anyone with a large dog knows, they need to keep their teeth to themselves. Any advice is much appreciated!